120598468
WHAT IS THE HAMILTONIAN FORMALISM
In this paper the basic concepts of the classical Hamiltonian formalism are translated into algebraic language. We treat the Hamiltonian formalism as a constituent part of the general theory of linear differential operators on commutative rings with identity. We take particular care in motivating the concepts we introduce. As an illustration of the theory presented here, we examine the Hamiltonian formalism in Lie algebras. We conclude by presenting a version of the orbit method in the theory of representations of Lie groups, which is a natural corollary of our view of the Hamiltonian formalism.
121453365
Nonlocal symmetries and the theory of coverings: An addendum to A. M. vinogradov's ‘local symmetries and conservation laws”
For a systemY of partial differential equations, the notion of a coveringŶ∞→Y∞ is introduced whereY∞ is infinite prolongation ofY. Then nonlocal symmetries ofY are defined as transformations ofŶ∞ which conserve the underlying contact structure. It turns out that generating functions of nonlocal symmetries are integro-differential-type operators.
115987350
The logic algebra for the theory of linear difierential operators
A material handling device on a sewing machine for feeding labels one at a time to a movable vacuum pickup head on the machine which moves the label to a position on the sewing machine adjacent the needle for sewing of the label onto a garment. The labels are cut from a strip wound on a reel. A reciprocable finger moves a portion of the strip along a surface and thereby unwinds the strip from the reel. On each label-feeding stroke of the finger, the strip is advanced a distance equal to the length or width of a label past a cutter and downwardly onto an elevator platform. The upper surface of the platform has at least one aperture therein which is connected to a vacuum source. The label is in a position on the platform covering the aperture and is held in position on the platform by vacuum from the vacuum source. With the label positioned and held on the platform, the cutter is actuated to cut the label from the remainder of the strip. While the cutter is cutting the label from the remainder of the strip, the elevator platform is simultaneously elevating the label to a position above the surface for subsequent pickup by the movable vacuum pickup head on the machine. As the pickup head moves into position to pick up the label, the vacuum is disconnected from the aperture in the platform so as to release its hold on the label and is connected to the pickup head. The pickup head by vacuum picks up the label and moves it from its position on the elevator platform to a position adjacent the needle for sewing of the label onto a garment. The elevator platform and cutter are lowered to their initial position. The finger then advances the strip a distance equal to the length or width of a label past the cutter and onto the platform. When the machine operator desires another label, the label is cut from the remainder of the strip, elevated, picked up, and positioned adjacent the needle and thereafter the next label is advanced past the cutter and onto the platform.
117769397
Symmetries of Partial Differential Equations : Conservation Laws - Applications - Algorithms
I (Acta Appl. Math. 15, 1-210).- Symmetries and Conservation Laws of Partial Differential Equations: Basic Notions and Results.- Symmetries and Conservation Laws of Kadomtsev-Pogutse Equations (Their computation and first applications).- Symmetries and Conservation Laws of Navier-Stokes Equations.- Symmetries, Invariant Solutions and Conservation Laws of the Nonlinear Acoustics Equation.- Local Nonintegrability of Long-Short Wave Interaction Equations.- On Symmetries and Conservation Laws of the Equations of Shallow Water with an Axisymmetric Profile of Bottom.- On Symmetries of the Heat Equation.- Nonlocal Trends in the Geometry of Differential Equations: Symmetries, Conservation Laws, and Backlund Transformations.- II (Acta Appl Math. 16, 1-142).- Exactly and Completely Integrable Nonlinear Dynamical Systems.- Recursion and Group Structures of Soliton Equations.- Building of Mathematical Models of Continuum Media on the Basis of the Invariance Principle.- III (Acta Appl. Math. 16,143-242).- Efficiently Implementing Two Methods of the Geometrical Theory of Differential Equations: An Experience in Algorithm and Software Design.- Computations in Differential and Difference Modules.- Reducing Systems of Linear Differential Equations to a Passive Form.- Software to Compute Infinitesimal Symmetries of Exterior Differential Systems, with Applications.- Lie Algebra Computations.
122513714
Brief note creep-stability analysis of viscoelastic cylindrical shells
The paper presents the creep-stability analysis of viscoelastic cylindrical shells under axial compression. The mechanical properties of the material are described by the constitutive equations of the linear viscoelastic theory in terms of convolution integral operators. The approximate analytical solution to the problem is obtained by means of a modification of the quasi-elastic method. As a result, the instability condition for the shell is formulated. It is shown that for viscoelastic materials with limited creep, there is a safe load limit below which the structure is asymptotically stable. Any load above the safe load limit leads to buckling at the corresponding critical time.
137026421
THE QUASI-ELASTIC METHOD IN CREEP STABILITY ANALYSIS
Abstract The paper presents a modification of the quasi-elastic solution technique aimed at applications to the stability analysis of viscoelastic structures. The study is concerned with two distinct instability phenomena, the bifurcation and the snapthrough buckling in the presence of creep. Respectively, two structural models are considered, a circular arch and a shallow two-bar system under sustained lateral loading. The quasi-elastic approximate solution results in the instability condition defined in terms of the load-critical time equation. The time-dependent response of the structures is studied in relation to the limited and unlimited creep behaviour of viscoelastic materials. Two numerical examples are given and accuracy of the method is discussed.