The asymptotic (non)equivalence of canonical and microcanonical ensembles, describing systems with soft hard constraints respectively, is a central concept in statistical physics. Traditionally, the breakdown ensemble equivalence (EE) has been associated nonvanishing relative fluctuations thermodynamic limit. Recently, it reformulated terms entropy density between probabilities. earliest observ...

Let R be a commutative Noetherian ring and let M be a nitely generated R-module. If I is an ideal of R generated by M-regular sequence, then we study the vanishing of the rst Tor functors. Moreover, for Artinian modules and coregular sequences we examine the vanishing of the rst Ext functors.

‎Let $G$ be a finite group‎. ‎We say that an element $g$ in $G$ is a vanishing element if there exists some irreducible character $chi$ of $G$ such that $chi(g)=0$‎. ‎In this paper‎, ‎we classify groups whose set of vanishing elements is exactly a conjugacy class‎.

Tour into the picture (TIP) proposed by Horry et al.[1] is a method for generating a sequence of walk-through images from a single reference picture (or image). By navigating a 3D scene model constructed from the picture, TIP produced convincing 3D effects. Assuming that the picture has one vanishing point, they proposed the scene modeling scheme called spidery mesh. However, this scheme has to...

This paper discusses optimality conditions for Borwein proper efficient solutions of nonsmooth multiobjective optimization problems with vanishing constraints. A new notion in terms contingent cone and upper directional derivative is introduced, a necessary condition the solution considered problem derived. The concept ε Abadie data qualification also which called strictly strong stationary obt...

Low-energy results from measurements of leptonic dipole operators are used to derive constraints on phases of the MSSM. After rediscovering older bounds on these phases, we try to investigate the impact of these possibly non-vanishing CP-odd phases on the measurement of CP-even cross-sections at the next lep-tonic collider.

In this paper, we study a class of Finsler metrics with orthogonal invariance. We find an equation that characterizes these Finsler metrics of almost vanishing H-curvature. As a consequence, we show that all orthogonally invariant Finsler metrics of almost vanishing H-curvature are of almost vanishing Ξ-curvature and corresponding one forms are exact, generalizing a result previously only known...

In this paper, we consider a nonsmooth multiobjective semi-infinite programming problem with vanishing constraints (MOSIPVC). We introduce stationary conditions for the MOSIPVCs and establish the strong Karush-Kuhn-Tucker type sufficient optimality conditions for the MOSIPVC under generalized convexity assumptions.

This paper studies the H 1 control problem for a nonlinear, unbounded, innnite dimensional system with state constraints. We characterize the solvability of the problem by means of a Hamilton-Jacobi-Isaacs equation, proving that the H 1 problem can be solved if and only if the HJI equation has a nonnegative viscosity supersolution, vanishing at the origin.