In this paper, some basic results concerning strict, nonstrict inequalities, local existence theorem and differential inequalities  have been proved for an IVP of first order hybrid  random differential equations with the linear perturbation of second type. A comparison theorem is proved and  applied to prove the uniqueness of random solution for the considered perturbed random differential eq...

We show lower bounds on the number of sample points and on the number of coin tosses used by general sampling algorithms for estimating the average value of functions over a large domain. The bounds depend on the desired precision and on the error probability of the estimate. Our lower bounds match upper bounds established by known algorithms, up to a mul-tiplicative constant. Furthermore, we g...

This paper presents an application of voting geometry to individual decision making. We demonstrate that a number of decision anomalies can arise as a natural consequence of the aggregation of preferences of different neural systems. We present a proof of existence of a set of voting procedures that can account for the attraction effect, the similarity effect and the compromise effect, and prov...

THIS SUPPLEMENTAL MATERIAL contains the proofs of all the lemmas that do not appear in the printed Appendix to the paper. It also contains the statements of all these lemmas and details of the intervening arguments in the proofs of the propositions. These arguments appeared in the printed Appendix. It also contains a proof of existence for a more general model that implies Proposition 3(ii). Th...

Entropy Methods for Identifying Hedonic Models This paper contributes to the literature on hedonic models in two ways. First, it makes use of Queyranne’s reformulation of a hedonic model in the discrete case as a network flow problem in order to provide a proof of existence and integrality of a hedonic equilibrium and efficient computational techniques of hedonic prices. Second, elaborating on ...

In 2002, a method has been proposed by Buchholz et al. in the context of Local Quantum Physics, to characterize states that are locally in thermodynamic equilibrium. It could be shown for the model of massless bosons that these states exhibit quite interesting properties. The mean phase-space density satisfies a transport equation, and many of these states break time reversal symmetry. Moreover...

We give a concise definition of mitered offset surfaces for nonconvex polytopes in R, along with a proof of existence and a discussion of basic properties. These results imply the existence of 3D straight skeletons for general nonconvex polytopes. The geometric, topological, and algorithmic features of such skeletons are investigated, including a classification of their constructing events in t...

We consider the stationary flow of a heat conducting Power Law shear thinning fluid in a bounded domain in R2. We present an elementary proof of existence of at least one weak solution.

‎using variational arguments‎, ‎we prove the existence of infinitely‎ ‎many solutions to a class of $p$-biharmonic equation in‎ ‎$mathbb{r}^n$‎. ‎the existence of‎ ‎nontrivial‎ ‎solution is established under a new‎ ‎set of hypotheses on the potential $v(x)$ and the weight functions‎ ‎$h_1(x)‎, ‎h_2(x)$‎.