text: At M3 Environmental Consulting, based in Monterey, California, we are experts in the field of indoor air quality testing. We possess all of the qualifications and certifications required by both the state of California and the EPA to perform proper testing and consulting. If you know the importance of air quality, then you’ll know why it’s important to have it inspected and tested by an established company.
  We provide environmental consulting services throughout Northern and Central California, and along California’s Central Coast. Our experience translates into quality service for our clients from private, public and governmental spheres. If you need indoor air quality testing conducted for your Monterey-based commercial property, private residence, school or otherwise, ensure you have proper testing performed by the specialists at M3 Environmental Consulting.
  Did you know that indoor air quality is often far worse than that of the outdoors? Because of closed systems such as an HVAC and the building structure itself, particulates and gases can become trapped and subsequently inhaled by occupants. Any use of toxic materials such as solvents, varnishes, adhesives, paints and glues can circulate throughout the enclosed space and cause harm. If you’re a property owner of any type, government agency, school district, or municipality, indoor air quality is most likely a concern. Obtain peace of mind by enlisting our expertise to establish air quality and develop a remediation plan.
  Our experienced technicians can test your indoor air for dangerous chemicals, harmful gases such as carbon monoxide, and microscopic organisms such as bacteria and mold. All of these contaminants can pollute your air with little to clue in the occupants, except perhaps for declining health, asthma attacks, allergies, unexplained fatigue, irritated lungs, and difficulty breathing. With small children or those with compromised immune systems such as the elderly or chronically ill, the effects of poor indoor air quality can be particularly harmful.
  Countless people suffer from poor air quality without knowing it. Air quality is often comprised by Volatile Organic Compounds (or VOCs). VOCs are carbon-based chemicals that evaporate at room temperature, and there are thousands of different VOC’s used and produced in our day-to-day lives. To makes thing more complicated, some of them have no odor and cannot be easily detected. Some common causes of poor indoor air quality include:
  Let M3 Environmental help ensure that the indoor air is as contaminate-free as possible. Our certified technicians will perform on-site inspections to determine any areas of contamination, and establish causes. After a thorough laboratory analysis of samples collected on-site, we’ll develop a full report, a remediation plan – and suggestions how to maintain a level of air quality. If you’re ready to breath easy and breath clean, call M3 Environmental today.
  Faà di Bruno’s formula is by far the best-known answer to the question: What is the mth derivative of a composite function? But it is not the only answer, and probably not the best answer; neither is it really Faà di Bruno’s answer, in the sense that at least three other mathematicians published it before him. We discuss the history of Faà di Bruno type formulas and the connections among them.
  In 1812 Laplace discovered, in his own words, a "résultat remarquable" that gives an integral formula for the reciprocal of the gamma function. We supply two simple proofs of this fundamental identity, which we exploit for a host of applications. These include an easy proof of the gamma function’s exponential decay in vertical strips and a derivation of summation formulas that are used to capture the Fourier coefficients of automorphic forms. As we demonstrate, these coefficients contain striking arithmetic information, which is indeed remarkable -- way beyond the sense of Laplace.
  Iterating a function like 1 + 1/x gives a sequence that converges to the Golden Mean but does so at a much slower rate than sequences derived from Newton’s method or the secant method. There is, however, a surprising relation among all these sequences. This relation, easily explained by the use of good notation, is generalized by means of Pascal’s "Mysterium Hexagrammicum." Throughout, we make contact with many areas of mathematics and physics including abstract groups, calculus, continued fractions, differential equations, elliptic curves, Fibonacci numbers, functional equations, fundamental groups, Lie groups, matrices, Möbius transformations, Pi, polynomial approximation, relativity, and resistors.
  Bi-infinite sequences of symbols occur in several different areas of mathematics, including symbolic dynamical systems and coding theory. The question of when two different sets of sequences are "the same" is fundamental. For example, by a simple renaming of the symbols, it is clear that the set of sequences consisting of any arrangement of zeros and ones is "the same" as the set of sequences consisting of any arrangement of a’s and b’s. Consider the set of sequences consisting of symbols {1,2,3,4 } satisfying the requirements that one and four can be followed only by one or three, and that two and three can be followed only by two or four. The fact that this set of sequences in also "the same" is not as obvious! In this paper, we consider examples drawn from two important classes, renewal systems and shifts of finite type. We discuss what it means for two sets of sequences to be the same and, with the help of our sharp-eyed snakes, we investigate several examples. The paper ends with the tantalizing open question of whether every shift
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