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## Abstract

The objective was to evaluate the quality and texture of all-beef summer sausages produced with varying degrees of fermentation, endpoint cooking temperatures, and high pressure processing (HPP) hold times. Across 3 replications, sausages were fermented and (Process A) cooked to pH 4.6 and thermally processed to 54.4°C with smokehouse chilling, (Process B) cooked to pH 5.0 and thermally processed to 54.4°C with smokehouse chilling, (Process C) cooked to pH 5.0 and thermally processed to 54.4°C with rapid ice bath chilling, (Process D) cooked to pH 5.0 and thermally processed to 48.9°C with rapid ice bath chilling, and (Process E) cooked to pH 5.0 and thermally processed to 43.3°C with rapid ice bath chilling. After chilling, the sausages were sliced, layered, vacuum packaged, and subjected to HPP at 586 MPa for 0, 1, 150, or 300 s. Post HPP, the sausages were evaluated for objective color (n = 9), lipid oxidation (n = 9), water activity (n = 9), texture profile analysis (TPA; n = 15), sensory analysis (n = 9), and proximate analysis (n = 9). Neither process (combination of pH and endpoint temperature) nor HPP affected lipid oxidation (P = 0.45 and P = 0.69, respectively). Process A resulted in a lighter color (P < 0.01) compared to the other process treatments. Additionally, Process A was less red (P < 0.01) than all other process treatments, and Processes D and E were the reddest (P < 0.01). TPA and trained sensory analysis indicated that, as endpoint temperature increased, so did sample hardness (P < 0.05). Springiness, cohesiveness, and gumminess decreased (P < 0.05) as the endpoint temperature decreased. Although springiness and gumminess increased (P < 0.05) with longer HPP hold times, the panelists were unable to detect differences among samples with longer hold times. The use of HPP at 586 MPa for up to 300 s may be incorporated into manufacturing processes for semidry beef summer sausages with limited impacts on color and texture.

Keywords: shelf-stable, sensory, sausage, cattle

How to Cite:

Rigdon M. & Thippareddi H. & McKee R. W. & Thomas C. L. & Stelzleni A. M., (2020) “Texture of Fermented Summer Sausage With Differing pH, Endpoint Temperature, and High Pressure Processing Times”, Meat and Muscle Biology 4(1). doi: https://doi.org/10.22175/mmb.9476

## Introduction

Consumers in the United States are seeking specialty food products and traditionally processed foods (Ilbery and Kneafsey, 1999; Guerrero et al., 2009) that historically would not meet current standards for thermal inactivation of pathogens. However, the Escherichia coli O157:H7 outbreak in commercially produced dry-cured salami (CDC, 1995) caused researchers and industry representatives (The Blue Ribbon Task Force of the National Cattlemen’s Beef Association) to outline a course of action aimed at mitigating the E. coli O157:H7 risk in such products (Reed, 1995) by achieving a 5-log reduction in E. coli O157:H7 populations. The majority of the methods suggested focused on thermal processing (Nickelson II et al., 1996). Alternatively, The Blue Ribbon Task Force also suggested that hurdle technology could be used in leu of, or in combination with, thermal processing for the reduction of pathogens (Nickelson II et al., 1996).

High pressure processing (HPP) is a technology that can aid in the reduction of pathogenic bacteria (Patterson et al., 1995; Cheftel and Culioli, 1997) and may be a viable option to meet the food safety performance standards requested by regulatory agencies (USDA, 2017) without requiring prior approval for use (USDA, 2012). However, inspection program personnel must verify that the hazard analysis supports the use and critical parameters of HPP (USDA, 2012). The performance standards suggest that establishments producing dry, fermented, and salt-cured products containing beef have scientific documentation demonstrating a 5D process (a process, or processes, that result in 5-log reduction under prescribed conditions for a given time or dose) for E. coli O157:H7 (USDA, 2017). HPP subjects the food substrate to extreme pressures (200 to 700 MPa; Campus, 2010) through forced water displacement (Cheftel and Culioli, 1997). Because pressure is created from forced water, the distribution of that pressure is isostatic, pseudo-instantaneous, and should not cause gross deformation, provided that there is not a significant amount of gas present in the food or package (Cheftel and Culioli, 1997). Although there should be no product deformation, the pressures achieved during HPP are enough to influence molecular changes and interactions, including weak hydrostatic interactions, hydrogen bonding, and hydrophobic bonds, as well as increasing protein denaturation, aggregation, and gelation (Messens et al., 1997; Campus, 2010). While the pressures created through HPP have been shown to reduce pathogens, including in dried and fermented meat products (Hugas et al., 2002; Morales et al., 2006; Omer et al., 2010; Scheinberg et al., 2014), little is known about the influence of HPP on the texture and color of fermented dry and semidry meat products containing beef. HPP has been shown to variably alter meat texture, tenderness, color, and oxidation stability dependent on rigor state, pressure setting, use of nitrate/nitrite, cooked state, and packaging type (Simonin et al., 2012). Therefore, the objective of this study was to investigate the influence of HPP in combination with total production process parameters (pH and endpoint cooking) on the texture and color of an all-beef fermented, semidry sausage product.

## Materials and Methods

### Beef trimmings procurement and batter processing

For each of 3 replicates, 20.4 kg of beef trimmings generated from previously frozen (20 ± 4 d of age) beef chuck rolls (Institutional Meat Purchase Specifications #116A; USDA Select) were blended to target 10% fat and were ground through a 12.7-mm plate. Trimmings were then ground a second time (4.76 mm) and placed into a reverse action mixer (Model A-80, Koch, Kansas City, MO). The ground trimmings were subsequently mixed for 1 min with a typical summer sausage seasoning blend including the following: 2% salt (Mortons, Chicago, IL); 0.8% or 0% dextrose (to achieve target pH values of 4.6 or 5.0, respectively, after fermentation); 0.25% sodium nitrite (156 parts per million [ppm]); 0.13% black pepper, white pepper, and garlic powder; 0.06% ginger, coriander, and mustard; and 0.05% sodium erythorbate (539 ppm). The batter was then inoculated with 10 g of thawed Pediococcus acidilacti starter culture (Kerry, Rochester, MN) diluted in 236 mL of distilled water (23°C ± 2°C) and mixed for an additional 2 min. The prepared batter was then placed into a vacuum stuffer (Vemag Robot 500, Reiser, Canton, MA), stuffed into fibrous mahogany casings of 5.08 cm in diameter (11 chubs) (Visko Teepak, Kenosha, WI), and clipped. After stuffing, 5 chubs were allocated to texture profile analysis (TPA), 3 chubs were allocated for color and lipid oxidation, and 3 chubs were allocated for sensory analysis. All chubs were then hung on a smoke cart and placed in an Alkar smokehouse (Model 8770-4-12000, Lodi, WI). Sausages were allowed to ferment at 43.3°C dry bulb with 85% relative humidity until the target endpoint pH was achieved. After fermentation, the dry bulb temperature was increased to 62.8°C with a relative humidity of 85% for 30 min and was then increased again to 73.9°C with 90% relative humidity for the remainder of the cooking cycle, and the sausages were cooked to an internal temperature of 43.3°C, 48.9°C, and 54.4°C followed by ice bath chilling. Two processing treatment groups, one from pH 4.6 and one from pH 5.0, were cooked to 54.4°C and cooled using a smokehouse cold-water shower for 10 min followed by refrigerated chilling methods to simulate industrial chilling, whereby the sausages were removed from the smokehouse after the cold shower and placed in a rapid chill ready-to-eat cooler at 1°C ± 1°C. The endpoint pH and cooking parameters were arranged into 5 different total processes, as follows: fermented to pH 4.6 and thermally processed to 54.4°C with smokehouse chilling (Process A), fermented to pH 5.0 and thermally processed to 54.4°C with smokehouse chilling (Process B), fermented to pH 5.0 and thermally processed to 54.4°C with rapid ice bath chilling (Process C), fermented to pH 5.0 and thermally processed to 48.9°C with rapid ice bath chilling (Process D), and fermented to pH 5.0 and thermally processed to 43.3°C with rapid ice bath chilling (Process E). The 5 treatment structures were evaluated as total processes that combined fermentation-level thermal processing with chilling procedures. After chilling, samples from all treatment groups were packaged and exposed to various HPP hold times at 586 MPa. HPP typically ranges from 300 to 600 MPa for meat pasteurization, dependent on the time and temperature during pressurization and the organism being targeted (Aymerich et al., 2008; Omar et al., 2010). Pressures close to 600 MPa have been shown to be the most effective against pathogenic E. coli (Gill and Ramaswamy, 2008; Omer et al., 2010; Simonin et al., 2012; Hygreeva and Pandey, 2016) and are commonly used for meat products in current industrial practices.

### HPP

After thermal processing and chilling, the sausages destined for TPA were cut to 5-cm lengths and vacuum packaged (B-620 series; 30–50 cm3O2/m2/24 h/101,325 Pa/23°C; Cryovac Sealed Air Corporation, Duncan, SC). The remaining chubs were sliced to 3.18 mm using a Hobart meat slicer (Model HS9, Hobart, Troy, OH), shingle packed, and vacuum sealed (Cryovac Sealed Air Corporation, Duncan, SC). The packages were then transported (0°C ± 2°C; 170 km) to Universal Pasteurization (Villa Rica, GA) and high pressure processed at 4°C ± 2°C and 586 MPa for 0, 1, 150, and 300 s. Samples processed for 0 s were packaged and transported with all other samples but remained in cold storage while other samples were subjected to HPP. One second was the amount of time for the HPP chamber to come up to 586 MPa and then release, which demonstrates the effects on summer sausage quality characteristics due to pressure alone. A common time under pressurization for meat products at the pressure used in the current study is between 150 and 180 s. Therefore, 150 s was selected to represent the lower end of a common time setting. The final HPP hold time (300 s) was selected to examine the impact of extended (double) time under pressurization on summer sausage quality.

### Proximate analysis

Samples from different HPP hold times were not different (P > 0.05) from each other for proximate analysis, therefore HPP hold time was composited by process treatment within each replicate to determine moisture and crude protein for the determination of the moisture-to-protein ratio (MPR). Total lipids were determined from the raw meat block. All analyses were performed in duplicate with a coefficient of variation less than 10.

Moisture was determined using disposable aluminum pans that were dried at 100°C in a forced-air oven (Fisher Scientific, Pittsburg, PA) overnight and equilibrated for 10 min in a desiccator. Pans were weighed, and 2.0 ± 0.1 g of homogenized sample was dried in duplicate at 100°C for 18 h (Soderberg, 1991). Samples were removed from the oven and allowed to cool for 10 min in the desiccator. Percent moisture was calculated as follows:

$%\text{\hspace{0.17em}}\mathrm{moisture}=\left[1\text{\hspace{0.17em}}-\text{\hspace{0.17em}}\left(\mathrm{dry}\text{\hspace{0.17em}}\mathrm{sample}\text{\hspace{0.17em}}\mathrm{weight}\text{\hspace{0.17em}}÷\text{\hspace{0.17em}}\mathrm{wet}\text{\hspace{0.17em}}\mathrm{sample}\text{\hspace{0.17em}}\mathrm{weight}\right)\right]\text{\hspace{0.17em}}×\text{\hspace{0.17em}}100%$

Crude protein was determined using a Nitrogen autoanalyzer (Leco FP-528 Nitrogen analyzer, Leco Company, St Joseph, MI) for the determination of N content (0.1 ± 0.05 g) and was expressed as percent crude protein (N content × 6.25). Total lipid content of the raw meat block was analyzed using wet tissue lipid extraction as outlined by Folch et al. (1957). Additionally, water activity was measured using an Aqualab water activity meter (Aqualab 4TE, Pullman, WA) immediately upon returning from HPP. Sausage pH was measured immediately after the fermentation step and was performed using a 1:10 dilution method in deionized water with an Oakton pH meter (Vernon Hills, IL; Koniecko, 1979).

### Lipid oxidation

Lipid oxidation was preformed using the rapid, wet method of thiobarbituric acid reactive species following the methods of Sinnhuber and Yu (1958) and Buege and Aust (1978) and modified according to Zipser and Watts (1962) and Shahidi et al. (1985) to account for the addition of sodium nitrite. Lipid oxidation was expressed as milligrams of malonaldehyde (MDA) per kilogram of meat.

### Objective color

Subsequent to HPP treatment, product was transported to the Meat Science and Technology Center (Athens, GA) under refrigeration, and vacuum-packaged slices were removed from the package and stacked 5 slices thick, making 3 stacks. Objective color was preformed using a Hunter-Lab MiniScan EZ (Hunter Associates Laboratory, Reston, VA) with illuminant A and a 10° viewing angle with a 32-mm aperture. Prior to use, the colorimeter was standardized with white, black, and saturated red tiles. Commission Internationale de l’Eclairage (CIE) L* (lightness), a* (redness), and b* (yellowness) were measured in triplicate and averaged. Cure color fading values were calculated using the reflectance at isosbestic wavelength ratios of R570:R650 (AMSA, 2012).

### Sensory

Trained sensory analysis was approved and conducted under Institutional Review Board No. STUDY00005493. An 8-member trained panel (AMSA, 2015) was used to evaluate the organoleptic properties. Samples were removed from the vacuum package, and 6 slices were cut into fourths and served on coded serving plates for consistent mastication orientation. Each panelist received 3 slices of each sample. A maximum of 16 samples were served each day across 2 sessions, with 3 h between the start of each session. Sliced quarters were served with a glass of distilled water and salt-free soda crackers for panelists to cleanse their palates between samples. Panelists sampled and recorded traits in a dark room with positive air flow and illuminated with red lighting to mask color. Once plated, samples were given to all panelists at the same time through a breadbasket with individual walls separating each panelist.

Slices were evaluated on the textural descriptors firmness, cohesiveness, springiness, and gumminess using a 15-cm line scale with anchors at 0, 7.5, and 15 (0 indicates the least intense and 15 is the most intense). The lines were anchored on both ends using various food products as reference points for the 0- and 15-cm points. The center of each line scale was anchored at 7.5 cm with a commercially available all-beef summer sausage. The extremity anchors for hardness, springiness, and cohesiveness were bologna, Now and Later candies, and SweeTARTS candies, respectively, for 0 cm and beef jerky, marshmallows, and Now and Later candies, respectively, for 15 cm. The benchmarks for gumminess were SweeTARTS candies for 0 cm and refrigerated gummy bears for 15 cm. The panelists were from a standing trained beef sensory panel. Panelists were further screened across 4 training sessions for their ability to identify and calibrate themselves to the standard anchors. After panelist screening and calibration, 2 additional sessions directed toward the measurement of various commercial meat products were included to ensure that panelists were accurately identifying each attribute consistently.

### TPA

Chilled samples (4°C) were removed from the package, and a hand-held coring device was used to extract a core of 1.27 cm (diameter) by 1.27 cm (length) from the geometric center of each sausage chub. Each core was centered on the platform of a TA-XT Texture Analyzer (Texture Technologies Corp., Hamilton, MA) and compressed to 50% of its original height by a 75-mm compression probe and a 25-kg load cell with a crosshead speed of 3.33 mm/s and a trigger force of 5 g. A 2-cycle sequence was used with a 5-s pause between compressions to allow for sample recovery. The TPA values were obtained from the graphed force-time curve output by Exponent Connect (Texture Technologies Corp., Hamilton, MA) for hardness, cohesiveness, springiness, gumminess, and chewiness.

### Statistical analysis

Data were analyzed using “Proc Mixed” of SAS (version 9.3, SAS Institute Inc., Cary, NC) as a randomized split-plot design, in which total process batch (pH and cooking temperature combination) was the whole plot and chub within process treatment batch was the sub-plot. HPP times were included as fixed effects, and replication was included as a blocking factor. Chub within process batch was considered the experimental unit, and slice(s) or core was considered the observational unit. Means were separated using the “LSmeans pdiff” option for main effects and the interaction of process treatment by HPP hold time. Means were considered different at α = 0.05.

## Results and Discussion

### Proximate analysis

Descriptive data for the sausage treatments are presented in Table 1. The percent fat in the raw meat block was not different between fermentation endpoints or replicates (P = 0.17 and P = 0.32, respectively). As expected, due to target endpoint pH and dextrose in the formulation, differences between fermentation endpoint pH for the treatments were achieved (P < 0.01). There were no differences for the MPR attributed to process treatment or HPP (P = 0.68, P = 0.63, respectively). HPP times did not affect the water activity (P = 0.60) of the product. Both process treatments cooked to 54.4°C and traditionally chilled (Processes A and B) had similar (P = 0.51) water activities. However, Processes B, C, and D were also similar to each other (P ≥ 0.06), with Processes C and D having lower (P ≤ 0.05) water activity than Process A. Process E had a higher (P ≤ 0.01) water activity than all other processes. Although there were statistical differences among processes for water activity, all processes were between 0.96 and 0.97, with minimal variation among replicates.

Table 1.

Least square means for proximate analysis parameters of all-beef summer sausage fermented and cooked to varying degrees of doneness

Water activity by cook temperature Moisture:protein by cook temperature
Target pH pH Fat % 54.4°C T1 54.4°C 48.9°C 43.3°C 54.4°C T1 54.4°C 48.9°C 43.3°C
4.6 4.60b 8.4 0.96c 3.0
5.0 5.03a 11.3 0.96bc 0.97b 0.97b 0.97a 3.0 3.0 3.1 3.1
SEM 0.02 1.39 0.001 0.001 0.001 0.001 0.07 0.07 0.07 0.07
• Indicates traditional smokehouse and cooler chilling methods. All remaining samples were chilled using rapid ice water chilling.

• Means within a heading with different superscripts differ (P < 0.05).

All treatments met US Department of Agriculture-Food Safety and Inspection Service requirements for a summer sausage product with pH 5.0 or less and an MPR of 3.1 or less (USDA, 2011). Similar to the differences in the water activity reported in the current project, Porto-Fett et al. (2010) described the water activity of fermented, cooked, and HPP semidry fermented meat, with differences of 0.06 as subtle. The small magnitude of differences in water activity combined with similar product MPR would not be expected to affect overall summer sausage quality.

### Lipid oxidation

There was not a process-by-HPP interaction (P = 0.46) for lipid oxidation. Furthermore, neither process nor HPP hold time impacted lipid oxidation (P = 0.07, P = 0.88 respectively). Due to the lack of differences for lipid oxidation, data are not presented in tabular form; however, samples ranged from 0.36 ± 0.06 to 0.60 ± 0.06 mg MDA/kg sausage, with an average of 0.47 mg MDA/kg sausage. Previous research has shown that HPP can have a negative effect on lipid oxidation and lipid stability of meat and meat products. The effect of HPP on lipid oxidation has been reported to be dependent on pressure setting, temperature during HPP, lipid amount and saturation index, product packaging, and whether the meat product was further processed (ready-to-eat, cooked, cured, dried) or fresh (Campus, 2010; Simonin et al., 2012; Hygreeva and Pandey, 2016). HPP can have a negative effect on the lipid stability of fresh meat samples, including beef, pork, and chicken (Cheah and Ledward, 1996; Ma et al., 2007; McArdle et al., 2010) both immediately after HPP and continuing through post-processing storage. According to the previously mentioned studies, the HPP parameters included temperatures in excess of 20°C, which was approximately 16°C above those used in the current study. Maintaining product in vacuum packaging or modified atmosphere packaging after HPP and at lower temperatures has been suggested to decrease the impact of HPP on lipid oxidation. Sun et al. (2017) reported no difference in lipid oxidation when vacuum-packaged beef steaks were subjected to HPP at 450 and 600 MPa for up to 15 min. Utama et al. (2017) found that vacuum-packaged beef steaks subjected to HPP at 600 MPa had greater lipid oxidation than steaks exposed to HPP at lower pressures (0.1, 200, and 400 MPa) and that lipid oxidation potential increased out to 6 d post processing. Contrary to the current research, Banerjee et al. (2017) reported differences in lipid oxidation between untreated mutton patties and patties processed at 200 and 400 MPa. Beltran et al. (2004) reported that minced poultry thigh samples subjected to pressurization under elevated temperatures had greater lipid oxidation than non-pressurized samples that were heated and refrigerated in aerobic conditions after 6 d of shelf life. However, there was no difference in lipid oxidation between pressurized and non-pressurized samples on d 1, indicating similar findings as the present study. In a follow-up study, Beltran et al. (2004) reported that when raw minced poultry thighs were pressurized at 500 MPa (−10°C to 50°C) for 30 or 60 min, there was no difference in lipid oxidation between the 30- and 60-min samples or after 1 or 9 d of anaerobic storage (4°C) but that cooked samples exhibited greater oxidation than uncooked samples. In the current study, the use of vacuum packaging plus the addition of nitrite in the formulation would prevent lipid oxidation during thermal processing, HPP, and further storage (Freybler et al., 1993).

### Objective color analysis

There was not a process-by-HPP time interaction (P ≥ 0.08) for any objective color measure (L*, a*, b*, and R570:R650 for cured color fading); therefore, the main effects of process and HPP time are shown in Tables 2 and 3, respectively. For L* values, Process A was lighter (P < 0.05) than all other treatment processes, which were similar to each other (P ≥ 0.17). HPP time did not impact sausage lightness (P = 0.29). Measurements of a* showed that Processes D and E, while similar to each other (P = 0.47), were more red (P < 0.05) than all other treatments. Treatments cooked to pH 5.0 and 54.4°C (Processes B and C), regardless of chilling, were similar in redness (P = 0.97) but were more red (P < 0.01) than Process A. HPP times indicated that, as time at 586 MPa increased, redness decreased (P < 0.05). However, the difference between 0 and 300 s was only 0.56 units.

Table 2.

Least square means for objective color scores for all-beef summer sausage cooked to varying degrees of doneness

Process A 53.21a 23.83c 14.58b 0.28a
Process B 52.24b 24.28b 14.57b 0.27b
Process C 52.43b 24.27b 14.56b 0.27b
Process D 51.96b 24.62a 14.89a 0.27b
Process E 52.12b 24.54a 14.92a 0.27b
Standard error 0.24 0.08 0.04 0.002
• Process A: pH 4.6 at 54.4°C with traditional smokehouse chilling; Process B: pH 5.0 at 54.4°C with traditional smokehouse chilling; Process C: pH 5.0 at 54.4°C with rapid ice bath chilling; Process D: pH 5.0 at 48.9°C with rapid ice bath chilling; Process E: pH 5.0 at 43.3°C with rapid ice bath chilling.

• Values determined by the following equation using isosbestic wavelengths: fade = 570 nm/650 nm (AMSA, 2012).

• Means within a column with different superscripts differ (P < 0.05).

Table 3.

Least square means for objective color scores for all-beef summer sausage high pressure processed at 586 MPa for varying hold times

High pressure hold time, s L* a* b* Fade1
0 52.13 24.56a 14.84a 0.27b
1 52.27 24.38ab 14.71b 0.27ab
150 52.48 24.24bc 14.67b 0.27ab
300 52.69 24.05c 14.60b 0.28a
Standard error 0.22 0.07 0.04 0.002
• Values determined by the following equation using isosbestic wavelengths: fade = 570 nm/650 nm (AMSA, 2012).

• Means within a column with different superscripts differ (P < 0.05).

The treatments cooked to a lower degree of doneness (Processes D and E) were similar to each other (P = 0.64) and were more yellow (P < 0.01) than the other processes, which were similar (P ≥ 0.77) to each other. Samples processed under HPP for any amount of time, while similar to each other (P ≥ 0.06), had lower b* values than the non-HPP controls (P < 0.05). Cured color fade (R570:R650) was greater (P < 0.01) in the sausages from Process A than all others, which were similar to each other (P ≥ 0.06). Furthermore, sausages subjected to HPP for 300 s had a more faded color (P < 0.01) than sausages that were not subjected to HPP. Sausages that underwent HPP for 1 or 150 s were similar (P ≥ 0.18) to those that were exposed to HPP for 0 and 300 s, respectively. Although there were differences regarding cured color fading, it is important to note that the greatest magnitude of difference was 0.01 units and likely not discernable to the naked eye.

It is likely that the majority of the overall color differences are due to the manufacturing process (pH and endpoint temperature) rather than the effects of HPP, as indicated by the differences found for L* between the processes but not the HPP times. Additionally, for a*, there was a greater magnitude of difference objectively observed as a result of process compared to the slight differences noted as a result of HPP. HPP can influence redness (indicated by its main effect of a*), but the difference is minimal and likely undetectable in subjective observation. Banerjee et al. (2017) found no difference between pressurized and non-pressurized mutton patties for the color parameters L*, a*, and b*, further substantiating the impact of cooking treatments over HPP on color parameters. Beltran et al. (2004) reported changes in the redness of minced chicken thighs; when pressure (500 MPa) was applied, the sample redness decreased. In addition, the authors reported a decrease in yellowness, although the decrease in yellowness was less remarkable than the decrease in redness. Although differences were unable to be detected in a* values with magnitudes greater than the current study (1.4 to 3.4 units), it is also important to note the elevated temperatures (5°C to 50°C) of the environment in which their chicken patties were processed compared to those of the current study (Beltran et al., 2004). As previously mentioned, the current study included sodium nitrite, heating, and acidification producing nitrosylhemochrome, which is a stable color under vacuum (AMSA, 2012). The present study also confirms that nitrosylhemochrome is stable through the HPP in cured and vacuum-packaged products that are subjected to pressures up to 586 MPa.

### Sensory analysis

An interaction for process by HPP time (P ≥ 0.58) was not observed for any of the texture attributes evaluated by the trained sensory panelists. The panelists were able to distinguish process effects for firmness (P < 0.01), springiness (P < 0.01), cohesiveness (P < 0.01), and gumminess (P < 0.01; Table 4). As expected, there was a stepwise increase in the firmness and gumminess detected by panelists as temperature and fermentation intensity increased. Process A was the firmest and gummiest (P < 0.01) product compared to all other processing treatments. The sausages fermented to pH 5.0 and cooked to 54.4°C, regardless of chilling method, were similar to each other in firmness and gumminess (P = 0.40). However, only the rapidly chilled samples were similar to the treatments cooked to 48.9°C (P = 0.15). Processes D and E were also similar to each other (P = 0.08), but Process E was less firm and gummy than Process C (P < 0.01).

Table 4.

Least square means for the sensory analysis of all-beef summer sausage cooked and fermented to varying degrees of doneness

Process1 Firmness2 Springiness2 Cohesiveness2 Gumminess2
Process A 8.4a 8.0a 8.6a 8.5a
Process B 7.8b 7.7ab 8.1b 7.9b
Process C 7.7bc 7.6bc 8.1b 7.9bc
Process D 7.4cd 7.5bc 7.9bc 7.5cd
Process E 7.1d 7.2c 7.8c 7.3d
Standard error 0.1 0.1 0.1 0.1
• Process A: pH 4.6 at 54.4°C with traditional smokehouse chilling; Process B: pH 5.0 at 54.4°C with traditional smokehouse chilling; Process C: pH 5.0 at 54.4°C with rapid ice bath chilling; Process D: pH 5.0 at 48.9°C with rapid ice bath chilling; Process E: pH 5.0 at 43.3°C with rapid ice bath chilling.

• Firmness, springiness, cohesiveness, and gumminess were measured on a 15-cm line scale with anchors at 0, 7.5, and 15 cm indicating least intensity, average intensity, and greatest intensity, respectively.

• Means within a column with different superscripts differ (P < 0.05).

Panelists also noted a stepwise increase in springiness as fermentation and cooking intensity increased (Table 4). Processes A and B were similar to each other (P = 0.09). However, Process A was springier than Processes C, D, and E (P < 0.05). Process B was similar to Processes C and D (P ≥ 0.31) but was springer than Process E (P < 0.01). Finally, Processes C, D, and E were all similar to each other (P ≥ 0.05). The sausages fermented to pH 4.6 and cooked to 54.4°C (Process A) were rated the most cohesive (P < 0.01), followed by the treatments fermented to pH 5.0 and cooked to 54.4°C and 48.9°C, regardless of chilling method (Processes B, C, and D, respectively), which were similar to each other (P ≥ 0.20). The sausages fermented to pH 5.0 and cooked to 43.3°C (Process E) were the least cohesive but were similar (P > 0.39) to the sausages from Process D. The trained panelists were unable to detect a difference in texture attributes in the sausages exposed to different HPP times (P ≥ 0.46; Table 5).

Table 5.

Least square means for the sensory analysis of all-beef summer sausage high pressure processed at 586 MPa for varying hold times

High pressure hold time, s Firmness Springiness Cohesiveness Gumminess
0 7.6 7.6 8.0 7.7
1 7.6 7.5 8.1 7.7
150 7.7 7.7 8.1 7.9
300 7.8 7.6 8.2 8.0
Standard error 0.1 0.1 0.1 0.1
• Firmness, springiness, cohesiveness, and gumminess were measured on a 15-cm line scale with anchors at 0, 7.5, and 15 cm indicating least intensity, average intensity, and greatest intensity, respectively.

Others have shown that increased temperatures were associated with a firmer and less tender product (Mathevon et al., 1995; Pohlman et al., 1997). Other attributes evaluated by the panelists in the current study showed similar results to that of firmness, in which an increased cooking intensity led to increased springiness, cohesiveness, and gumminess. Additionally, Marcos et al. (2007) reported that trained sensory panelists, when evaluating the hardness and gumminess of low-acid fermented sausages, were unable to distinguish differences between pressurized and unpressurized fermented sausages. Mor-Mur and Yuste (2003) performed triangle tests comparing pressurized fermented sausages to heat-treated fermented sausages, finding that, in all cases, panelists preferred the pressurized samples over the heat-treated samples, describing them as less grainy and more uniform in texture. Although the literature is limited at present, the inability of trained sensory panelists to discern textural differences among HPP processing times should give processors confidence that the use of HPP would not affect sensorial perceptions.

### TPA

Similar to the trained sensory analysis, there was not a process-by-HPP time interaction (P = 0.47) for TPA. The main effects for TPA due to cooking treatment and HPP time are presented in Tables 6 and 7, respectively. The differences among processes for hardness of the sausages when measured by TPA followed a trend similar to that of the sensory firmness. Process A was harder (P < 0.01) than the other processes. Processes C and D were similar (P = 0.47) in hardness; however, only Process C was similar to Process D (P = 0.13). Additionally, Processes D and E were similar (P = 0.17), even though Process E was less hard (P < 0.01) than C. Similar to sensory analysis, hardness as measured by TPA was not impacted by HPP time (P = 0.10).

Table 6.

Least square means for the instrumental texture analysis of all-beef summer sausage cooked and fermented to varying degrees of doneness

Process1 Hardness (N) Springiness (%) Cohesiveness Gumminess Chewiness
Process A 66.3a 63.5ab 0.324a 21.1a 1,340a
Process B 55.4b 65.0a 0.292b 16.1b 1,053b
Process C 54.0bc 63.8ab 0.286b 15.4bc 986bc
Process D 50.9cd 62.7b 0.286b 14.4cd 907cd
Process E 48.2d 60.2c 0.296b 14.1d 854d
Standard error 1.6 0.6 0.006 0.4 30
• Process A: pH 4.6 at 54.4°C with traditional smokehouse chilling; Process B: pH 5.0 at 54.4°C with traditional smokehouse chilling; Process C: pH 5.0 at 54.4°C with rapid ice bath chilling; Process D: pH 5.0 at 48.9°C with rapid ice bath chilling; Process E: pH 5.0 at 43.3°C with rapid ice bath chilling.

• Means within a column with different superscripts differ (P < 0.05).

Table 7.

Least square means for the instrumental texture analysis of all-beef summer sausage high pressure processed at 586 MPa for various hold times

High pressure hold time, s Hardness (N) Springiness (%) Cohesiveness Gumminess Chewiness
0 55.7 62.9ab 0.296 16.4ab 1,040a
1 52.5 61.8b 0.293 15.3c 949b
150 54.9 63.4a 0.295 16.1bc 1,025a
300 56.8 64.0a 0.302 17.1a 1,098a
Standard error 1.5 0.5 0.013 0.4 27
• Means within a column with different superscripts differ (P < 0.05).

The sample recovery in height after the first compression and before the second compression is an indication of springiness. The treatments cooked to 54.4°C, regardless of pH or cooling method (Processes A, B, and C), were similar to each other (P ≥ 0.08) and springier (P < 0.01) than Process E sausages. Unlike sensory analysis, HPP hold time did influence springiness (P < 0.05). Hold times of 300, 150, and 0 s were similar to each other (P ≥ 0.19), whereas samples held for 300 and 150 s were springier (P < 0.01) than those held for 1 s. There was no difference (P = 0.09) in sample springiness for hold times between 0 and 1 s.

The sausages from Process A were more cohesive (P < 0.01) than the others, and all other processes were similar to each other (P ≥ 0.18). Cohesiveness was not affected by HPP time (P = 0.62), again following the same trend as that recorded from sensory analysis. Gumminess, a product’s hardness as it relates to its ability to stay together, was influenced by both cooking treatment and HPP hold time (P < 0.01). The sausages fermented to pH 4.6 (Process A) were the gummiest (P < 0.01), while the products fermented to 5.0 and cooked to 54.4°C, regardless of cooling method (Processes B and C), were similar to each other (P = 0.20) but gummier (P < 0.05) than the sausages cooked to 43.3°C (Process E). Processes C and D were similar (P = 0.10), with only Process D being similar to E (P = 0.55). HPP hold times of 300 and 0 s were similar for gumminess (P = 0.17). The treatments receiving 150 s of hold time during HPP were less gummy (P < 0.05) than those receiving 300 s of hold time, even though 150 s of hold time was similar (P> 0.06) to both 0 and 1 s.

Process and HPP hold time influenced chewiness (P < 0.01) and followed a similar trend for process as gumminess. Process A was the chewiest (P < 0.01), and Processes D and E were similar to each other (P = 0.14) and less chewy (P < 0.05) than the other treatments. Furthermore, Processes B and C were similar to each other (P = 0.06). Treatments receiving 300-s HPP were chewier (P < 0.05) than the other treatments. Sausages subjected to HPP for 0 and 150 s were similar (P = 0.68) in chewiness and were chewier (P < 0.05) than samples processed for 1 s.

Hardness results were in agreement with sensory panelist observations of hardness/firmness, springiness, cohesiveness, and gumminess. Instrumental texture analysis also agreed with sensory panelist evaluations in regard to HPP hold times for hardness and cohesiveness. Mor-Mur and Yuste (2003) reported no difference for hardness or springiness when unprocessed cooked sausages were compared to ones subjected to HPP at 500 MPa for 300 s. Their findings were attributed to the industrial cooking process causing gelation within the sausage, as well as subsequent pressure processing having only the ability to induce exudation, minorly impacting texture. Pressurization parameters used by Mor-Mur and Yuste (2003) included temperatures of 65°C, well above the heating parameters used in the current study, which could have increased protein gelation and subsequent hardening during the pressurization process. Marcos et al. (2007) reported an increase in cohesiveness, chewiness, and springiness during the pressurization of low-acid fermented sausages. Their parameters included HPP temperatures (17°C) above those used during their ripening process, which could have increased the ultimate temperature of the sausage. As noted in this study by the difference between Processes C, D, and E, the ultimate temperature endpoint does have an effect on sausage texture. Although few manuscripts exist describing the texture of low-acid fermented sausages subjected to HPP, data show that, while HPP might have an effect on sausage texture, the main force exerting control over texture is product ultimate temperature.

## Conclusions

Summer sausage products that received less rigorous fermentation and thermal processing were less firm, springy, cohesive, and gummy than summer sausage products fermented and cooked to industry-validated endpoints (pH 4.6 and thermally processed to 54.4°C). The use of HPP at 586 MPa for up to 300 s did not influence the ability of trained sensory panelists to differentiate among the products even though there were slight differences for springiness, gumminess, and chewiness with evaluation by objective TPA. Although there were some differences in objective color attributed to cooking treatment and HPP hold times, the differences were minimal, and it is questionable whether they would be subjectively differentiated. HPP at 586 MPa for up to 300 s may be incorporated into a food safety plan without impacting sensory and texture attributes.

## Acknowledgements

This work was supported by Grant No. 2012-68003-30155 and Grant No. 2011-68003-30012 from the USDA National Institute of Food and Agriculture, Agriculture and Food Research Initiative Foundational Program.

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# Score: 0 of 6 pts 2 of 4 (0 complete) HW Score E18-17 (similar to) Selected...

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data for three companies are given below All inventory amounts are ending balances and all amounts are in milions Data Table Cash 25 35 company B 13 Wages Expense 35 Equipment 9 Accounts Receivable 18 Service Revenue 7 Cash 62 Rent Expense Company C Administrative Expenses Cash Net Sales Revenue Net Sales Revenue Finished Goods Inventory Cost of Goods Sold Selling Expenses Equipment 1 40 Se ng EXPRISES 24 Merchandise inventory 11 Equipment Work-in-Pro inventory Accounts Receivable Cost of Goods Sold Accounts Recervable Cost of Goods Manufactured Administrative Expenses Raw Materials inventory Print Done e from any list or enter any number in the input fields and then click Check Answer Clear All Check Answer aining

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Arun, Gulab, Neel and Shweta must choose one shirt each from a pile of four shirts coloured red, pink, blue and white respectively. Arun dislikes the colour red and Shweta dislikes the colour white. Gulab and Neel like all the colours. In how many different ways can they choose the shirts so that no one has a shirt with a colour he or she dislikes?

1. $21$
2. $18$
3. $16$
4. $14$

edited | 4.4k views

Total possibilities $=4! = 24.$

No. of ways  'Arun chooses red' or 'Shwetha chooses white'

$=\text{(no.of ways Arun chooses red')}$
$+ \text{(no.of ways Shwetha chooses white')}$
$-(\text{no.of ways Arun chooses red' and Shwetha chooses white')}$

$=6+6-2 = 10$

required $=24-10=14.$

Correct Answer: $D$
by Active (1.4k points)
edited
+1
nice one..
0
Why you subtracted 2 in 6+6-2.

My point is if A got red and S got white ,it should also removed from 4!.

0

0
Nice explanation
+1
Why can't it be 3 x 4 x 4 x 3 = 144 ?

Question doesn't say that two or more person can't have same colored shirts.

Aren't the options given wrong?
+3

see the question again - "pile of four shirts" .i.e, there are only four shirts to choose from.

Ans will be D) 14

case 1 if Arun takes  pink then shweta can take either red or blue (so 2 choices) and gulab or neel have 2 and 1 choice respectively

so total ways in this case =2x2x1=4

Case 2

if Arun takes  blue then shweta can take either red or pink (so 2 choices) and gulab or neel have 2 and 1 choice respectively

so total ways in this case =2x2x1=4

Case 3

if Arun takes  white  then shweta can take either red or pink or blue (so 3 choices) and gulab or neel have 2 and 1 choice respectively

so total ways in this case =3x2x1=6

total  =4+4+6 =14 cases
by Active (2.3k points)
Another ways is

(1) When Arun takes white color then  1*3*2*1 (Arun *  Gulab *  Neel * Shweta) = 6

(2) When Arun does not takes white color then 2*1*2*2 (Arun *  Gulab *  Neel * Shweta) = 8

So Total is 8+6 = 14. Answer is (D) Part.
by Boss (13.7k points)
3p1 +4p1+4p1+3p1=14( as gulaab and neel can select any color of shirt  while arun and shweta can have only 3 shirt to choose )
by Active (1.1k points)

Simplest Approach

by Junior (923 points)


text:
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18
Posted byu/[deleted]8 years ago
Archived

## Is this consequential, or simply incidental?

64% Upvoted
Sort by
level 1
57 points · 8 years ago

I am not sure I understand the question completely but the Laplace transform is regularly seen as a generalization of the Fourier transform.

level 2
16 points · 8 years ago · edited 8 years ago

Uptroped. The Fourier Transform can be considered as as the Laplace Transform evaluated along the imaginary axis.

Edit: The Fourier Transform can be obtained straightforwardly from the Laplace Transform by substituting s = jw, where w = 2 pi f

This is a handy thing to keep in mind when looking at the locations of poles and zeros in the complex plane and considering their influence upon the system frequency response.

level 3
[deleted]
1 point · 8 years ago

Interesting, I wonder what happens if you restrict s to other paths in C. Well, I guess nothing happens, you can only evaluate F(s) at certain points in that case. I guess thats not too interesting, unless it had applications like the Fourier transform.

level 3
[deleted]
1 point · 8 years ago

Gotcha.

So, what's our current understanding S domain embodied in real life?

level 2
4 points · 8 years ago

I always heard it as the Fourier transform being a special case of the Laplace transform... guess it depends what sequence you go through first.

level 3
13 points · 8 years ago

The Fourier transform was developed first, I believe. So calling Laplace transform a generalization would be consistent. But it's 6 of one, 1/2 dozen of the other.

level 3
2 points · 8 years ago

Same here.

level 3
[deleted]
-1 points · 8 years ago

Technically, aren't both part of the same generalized tranform? That is:

∫f(t)exp[-(s+2πiξ)t]dt

Which is 'complete' in the sense that (s+2πiξ) is fully complex with independent parts?

level 4
3 points · 8 years ago

If s is complex, that's not any different than the laplace transform. It's just written a different way. If s is real, then you're just breaking down the laplace transform into real and imaginary parts. Either way, it's the laplace transform with different notation.

level 5
[deleted]
5 points · 8 years ago

I knew I made you orange for a reason.

level 2
[deleted]
1 point · 8 years ago

That page is, as always, informative as it can be without becoming the textual equivalent of a 300 page book.

I think the specific question I'm asking here, is: if we cannot fathom the imaginary domain, why not give the s-domain a try?

level 1
8 points · 8 years ago

A laplace transform is taken from 0-infinity, not from -infinity to infinity.

This is important. A reverse laplace transform is a complex contour integral, and the laplace contour is a line parallel with the imaginary axis, encompassing everything to the right of it. Consequentially, what this means is that events can only happen to things after it, or that events can only travel forward in time, and not backwards in time. This is why a laplace transform is so useful for dealing with time, as opposed to space.

A fourier transform can be described as a bilateral, or "two-way" laplace transform directly over the imaginary axis.

level 2
[deleted]
1 point · 8 years ago

A laplace transform is taken from 0-infinity, not from -infinity to infinity.

This is the Laplace transform referenced.

level 1
4 points · 8 years ago

What are you trying to imply? I don't understand this at all.

level 2
2 points · 8 years ago

Well, I'm not a mathematician, but I think what he's on about is how s 'maps' (however you'd call it) to -2πiξ. 'π' (pi) is a constant, as is 'i', as is -2.

He didn't know if it was a coincidence.

The actual math is... like, I don't do that stuff, right? So, it's not shining brightly obvious to me the way it may to someone who understood the equations. However, what I get from the gist of the reactions is that probably, no, it's not a coincidence.

level 3
[deleted]
1 point · 8 years ago

I read this in an Australian accent and it was fantastic

level 2
[deleted]
1 point · 8 years ago

Me either. Of course, my math has gotten shaky over the years.

level 1
1 point · 8 years ago

The Laplace transform can be derived from the Fourier transform by multiplying the input function by an exponential, e-\sigma, then taking the Fourier transform.

level 1
1 point · 8 years ago

I'm not sure why 2 pi i xi is pure imaginary. It seems like it too would be complex.

Also it rhymes well.

level 2
1 point · 8 years ago

Cos xi and t are both real, by definition.

level 1
1 point · 8 years ago · edited 8 years ago

I would argue that this is consequential. The Fourier transform is a decomposition into sinusoidal basis functions. In some sense, the input and output have the same amount of information. This has a lot of practical, computational uses. E.g. If your input signal is repeating (informally, this means duration-limited for practical uses) and discrete time, I can use the Fourier transform to convert it into a finite set of numbers, compute over those numbers, and convert it back. Very powerful computational tool.

The Laplace transform is over the entire complex number plane. It is a much more powerful tool for intuitive or symbolic analysis. I can do stability analysis. Concepts like "no poles in the right half plane" are fundamental to the Laplace formulation, and meaningless in the Fourier formulation. This isn't just one trick (read about conformal mappings, Nyquist stability criterion, complex derivatives, etc.). On the other hand, I can't reasonably compute with it -- I have functions over the entire complex number plane, and there's no clear way how I would represent that in a computationally efficient way (or at least not if I'm trying to use it in any way beyond as a Fourier transform).

level 1
1 point · 8 years ago · edited 8 years ago

As another redditor already wrote, the Fourier transform is indeed seen as a special case of the Laplace transform. But why the common form with an integral and a product of the function with another one?

To put it simply, for two functions |f>,|g> in a vector space of functions over some interval (which might need some properties, I don't know), a scalar product between those (that is, a map of that vector space squared to a scalar, written as <f|g>) is something like an integral f*(x)g(x)dx over this interval (with f* the conjugate-complex of f).

If there is a complete orthonormal base {f_n} in this vector space, <f_n|g> |f_n>=c_n |f_n> is something like the projection of the function g onto the function f_n (where n might be a discrete or continuous index). The completeness property of our f_n functions/vectors means that we can reconstruct the original function g from all these projections together (with a sum or integral), which is why we can use the Laplace or Fourier transform without worry that we might not get our function back.

level 1
1 point · 8 years ago

THEN WHO WAS FOURIER?

But seriously you are assuming s to be purely imaginary, it could be real.

level 2
[deleted]
-1 points · 8 years ago

No, no. Complex does not predicate a number be purely imaginary. Rather, it refers to the inclusive domains of both real and imaginary number lines, including the value of "0" located on each of the lines that also demarcates their intersection, as defined by convenience.

level 3
0 points · 8 years ago

That's what I said?

level 1
[deleted]
0 points · 8 years ago

You could just as well have a Fourier transform with a pure real exponent, but then you're decomposing your waveform into exponentials, rather than sin waves, which isn't nearly as useful.

level 2
2 points · 8 years ago · edited 8 years ago

you're decomposing your waveform into exponentials, rather than sin waves, which isn't nearly as useful

It is to mathematicians! From a mathematician's, or at least a representation theorist's, point of view, exponentials are the only homomorphisms [; \mathbb R \to \mathbb C\cross ;], hence are marvellous; whereas trigonometric functions are just solutions to [; y'' = -y ;], hence are less exciting.

EDIT: I forgot to indicate that I was talking about homomorphisms to [; \mathbb C\cross ;] (multiplicative), not [; \mathbb C ;] (additive).

level 3
[deleted]
1 point · 8 years ago

Trigonometric functions are the only (continuous) homomorphism from the additive reals to the complex unit circle.

level 4
1 point · 8 years ago

Huh? Trigonometric functions (by which I mean sine, cosine, and such) are not homomorphisms, in the sense that [; sin(x + y) \ne sin(x)\sin(y) ;]. Perhaps you mean that the map [; x \mapsto (\sin(x), \cos(x)) ;] is a homomorphism? This is certainly true, but it's just the complex exponential [; x \mapsto e{-ix + \pi/2} ;].

(I think that continuity is redundant when discussing characters of [; \mathbb R ;], but I'm not quite sure; certainly it's true for homomorphisms [; \mathbb R \to \mathbb R ;].)

level 5
[deleted]
1 point · 8 years ago

Yes, I meant complex exponentials. Sine and cosine don't map to complex circle. (You're probably right that continuity is redundant.)

level 6
1 point · 8 years ago

Oh, I see! Were you pointing out that I'd accidentally said I was mapping into the additive, not the multiplicative, group?

level 7
[deleted]
1 point · 8 years ago

No I knew what you meant (I think). My point was that there is nice characterization of trigonometric functions as homomorphisms [; \mathbb{R} \to \mathbb{T} ;] and there is also a characterization of exponentials in terms of differential equations so I don't know why one should be less exciting than the other. tl;dr I think Fourier transforms and (two-sided) Laplace transforms are basically the same thing.

level 8
1 point · 8 years ago

Sorry, I think that I must be really missing what you're saying.

there is also a characterization of exponentials in terms of differential equations

Certainly, I agree. I'm a representation theorist, not a PDE guy, so it doesn't appeal to me; but, hey, more power (ha!) to exponentials.

My point was that there is nice characterization of trigonometric functions as homomorphisms [; \mathbb{R} \to \mathbb{T} ;]

However, I thought we agreed above that trigonometric functions don't even map into the unit circle—unless we mean something different by trigonometric functions (I mean sine, cosine, and their various quotients).

level 2
1 point · 8 years ago

This is incorrect.

level 1
-1 points · 8 years ago

my vote's on incidental factoid. a similar relationship exists for other transforms too (eg. z-transform used in discrete signal processing)

level 1
-4 points · 8 years ago

??

level 1
Comment deleted8 years ago(0 children)
level 2
3 points · 8 years ago

Why did you bother posting anything then?

level 3
[deleted]
3 points · 8 years ago

I posted a similar comment. Like blue_strat, I'd like to understand the meaning of the formula in relation to the post. I subscribed to /r/math because I wanted to learn new/interesting/relevant stuff about mathematics.

I realize that to properly understand what's going in the image requires dedicated study and more rigorous courses than what I had to take in my undergrad. But, does that mean that no one can explain it in layman's terms?

Is it not okay that some people are ignorant and would like to have an explanation so they can better understand? Or is this subreddit only for mathematicians who understand the context of every post? Because, if the subscribers here are that unfriendly and unwelcoming, I'm sure I can find a similar alternative.

level 3
-2 points · 8 years ago

Why did you bother posting a response to a poster that doesn't understand the post just to question his motives for posting?

level 4
[deleted]
3 points · 8 years ago

Why... oh nevermind.

level 5
0 points · 8 years ago

:)

level 2
1 point · 8 years ago

To the responses: this was on the front page, and I didn't notice that it was from /r/maths, and that subsequently this comment would look as it did, as a drop of outsider ignorance in a sea of familiarity.

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text:
• Create Account

### #Actualkloffy

Posted 14 March 2013 - 01:08 PM

This should be pretty basic template meta programming, but everything I have found on Google isn't quite the thing I am looking for. Suppose I have a template with an empty body that users can specialize:

template<typename Target, typename Source, typename Enable = void>
struct conversion
{
static const bool value = false;

static Target to(Source const& value);
static Source from(Target const& value);
};

And a possible specialization might look like this:

template<typename Target>
struct conversion<Target, std::string>
{
static const bool value = true;

static Target to(std::string const& value)
{
return boost::lexical_cast<Target>(value);
}

static std::string from(Target const& value)
{
return boost::lexical_cast<std::string>(value);
}
};

Now, I can check whether a conversion exists by checking conversion<Target, Source>::value. However, I would like to simplify this further, eliminating the need to explicitly define the integral value constant. This can probably be done using a check like sizeof(?) == sizeof(char). However, since there are a few pitfalls, I wonder if someone could point me towards the "best practice" approach.

### #2kloffy

Posted 14 March 2013 - 01:07 PM

This should be pretty basic template meta programming, but everything I have found on Google isn't quite the thing I am looking for. Suppose I have a template with an empty body that users can specialize:
template<typename Target, typename Source, typename Enable = void>
struct conversion
{
static const bool value = false;

static Target to(Source const& value);
static Source from(Target const& value);
};
And a possible specialization might look like this:
template<typename Target>
struct conversion<Target, std::string>
{
static const bool value = true;

static Target to(std::string const& value)
{
return boost::lexical_cast<Target>(value);
}

static std::string from(Target const& value)
{
return boost::lexical_cast<std::string>(value);
}
};
Now, I can check whether a conversion exists by checking conversion<Target, Source>::value. However, I would like to simplify this further, eliminating the need to explicitly define the integral value constant. This can probably be done using a check like sizeof(?) == sizeof(char). However, since there are a few pitfalls, I wonder if someone could point me towards the "best practice" approach.

### #1kloffy

Posted 14 March 2013 - 01:06 PM

This should be pretty basic template meta programming, but everything I have found on Google isn't quite the thing I am looking for. Suppose I have a template with an empty body that users can specialize:

template<typename Target, typename Source, typename Enable = void>
struct conversion
{
static const bool value = false;

static Target to(Source const& value);
static Source from(Target const& value);
};
And a possible specialization might look like this:
template<typename Target>
struct conversion<Target, std::string>
{
static const bool value = true;

static Target to(std::string const& value)
{
return boost::lexical_cast<Target>(value);
}

static std::string from(Target const& value)
{
return boost::lexical_cast<std::string>(value);
}
};
Now, I can check whether a conversion exists by checking conversion<Target, Source>::value. However, I would like to simplify this further, eliminating the need to explicitly define the integral value constant. This can probably be done using a check like sizeof(?) == sizeof(char). However, since there are a few pitfalls, I wonder if someone could point me towards the "best practice" approach.

PARTNERS


text:
# Measurements of prompt charm production cross-sections in pp collisions at √s=13 TeV

LHCb Collaboration

Research output: Contribution to journalArticle (Academic Journal)

### Abstract

Production cross-sections of prompt charm mesons are measured with the first data from $pp$ collisions at the LHC at a centre-of-mass energy of $13\,\mathrm{TeV}$. The data sample corresponds to an integrated luminosity of $4.98 \pm 0.19\,\mathrm{pb}^{-1}$ collected by the LHCb experiment. The production cross-sections of $D^{0}$, $D^{+}$, $D_{s}^{+}$, and $D^{*+}$ mesons are measured in bins of charm meson transverse momentum, $p_{\mathrm{T}}$, and rapidity, $y$, and cover the range $0 <p_{\mathrm{T}} <15\,\mathrm{GeV}/c$ and $2.0 <y <4.5$. The inclusive cross-sections for the four mesons, including charge conjugation, within the range of $1 <p_{\mathrm{T}} <8\,\mathrm{GeV}/c$ are found to be $$\sigma(pp \to D^{0} X) = 2072 \pm 2 \pm 124\,\mu\mathrm{b}\\ \sigma(pp \to D^{+} X) = 834 \pm 2 \pm \phantom{1}78\,\mu\mathrm{b}\\ \sigma(pp \to D_{s}^{+} X) = 353 \pm 9 \pm \phantom{1}76\,\mu\mathrm{b}\\ \sigma(pp \to D^{*+} X) = 784 \pm 4 \pm \phantom{1}87\,\mu\mathrm{b}$$ where the uncertainties are due to statistical and systematic uncertainties, respectively.
Original language English 159 (2016) 46 Journal of High Energy Physics 2016 Published - 22 Mar 2016

### Bibliographical note

Includes comments of erratum JHEP 09 (2016) 013 and an additional erratum JHEP 05 (2017) 074. All figures and tables, along with any supplementary material and additional information, are available at https://lhcbproject.web.cern.ch/lhcbproject/Publications/LHCbProjectPublic/LHCb-PAPER-2015-041.html

• hep-ex


text:
# Arithmetic distribution

A discrete probability distribution concentrated on a set of points of the form $\pm nh$, where $h>0$ and $n=1,2,\ldots$. It is a special case of a lattice distribution.


text:
## Linear Algebra: A Modern Introduction

$(x,y,z)=(5t+2,2t-1,t)$; $t$ refers to a real number.
Consider $y-2z=-1 \implies y=2z-1$ Suppose $z=t$ This implies $y=2t-1$ Now, $x-3y+z=5 \implies x-3(2t-1)+t=5$ or, $x=5t+2$ Our result is : $(x,y,z)=(5t+2,2t-1,t)$; $t$ refers to a real number.