In this paper, a nonlinear elliptic boundary value problem with singular nonlinearity Lu(x) = f(x, u(x)), x ∈ Ω, u(x) = φ(x), x ∈ ∂Ω, is studied, where L is a uniformly elliptic operator, Ω is a bounded domain in R , N ≥ 2, φ ≥ 0 may take the value 0 on ∂Ω, and f(x, s) is possibly singular near s = 0. Some results regarding the existence of positive solutions for the problem are given under a s...

In this article, we give a criterion for an embedding of a projective variety to be deened by quadratic equations and for it to have linear syzygies. Our criterion is intrinsic in nature and implies that embedding corresponding to a suuciently high power of any ample line bundle will have linear syzygies up to a given order. Introduction. Let X be a projective variety. The conditions that guara...

We present a new kind of simulation with the aim of using it as minimality criterion for models of modal logics. We discuss such minimality criterion by comparing it with minimal modal Herbrand models. Even though our final goal is the automated generation of minimal models through a tableau-based method, this paper is on a theoretical level and does not aim to propose algorithms on how to gene...

We consider an Ising system in d 2 dimensions with ferromagnetic spin-spin interactions ?J (x; y)(x)(y), x, y 2 Z d , where J (x; y) scales like a Kac potential. We prove that when the temperature is below the mean eld critical value, for any small enough (i.e. when the range of the interaction is long but nite), there are only two pure homogeneous phases, as stated by the van der Waals theory....

For a set-valued stochastic sequence (Gn)Nn=0 with relatively open convex values Gn(ω) we give a criterion for the existence of an adapted sequence (xn)Nn=0 of selectors, admitting an equivalent martingale measure. Mentioned criterion is expressed in terms of supports of the regular conditional upper distributions of the elements Gn. This result is a refinement of the main result of author’s pr...

Multiplicity of sets of soft jets with energies ranging in some interval is determined. The possible role of collective effects is discussed. The phenomenon of jet emission is well known in QCD and firmly established in experiment. The two-jet events in e + e −-annihilation provide us with unique possibility to measure jets with fixed energy equal to that of colliding particles. In all other ca...

Atoms and the planets acquire their stability from the quantum mechanical incompatibility of the position and momentum measurements. This incompatibility is expressed by the fundamental commutator [x, px] = ih̄, or equivalently, via the Heisenberg’s uncertainty principle ∆x∆px ∼ h̄. A further stability-related phenomenon where the quantum realm plays a dramatic role is the collapse of certain sta...

We establish a new spectral criterion for Kazhdan’s property (T ) which is applicable to a large class of discrete groups defined by generators and relations. As the main application, we prove property (T ) for the groups ELn(R), where n ≥ 3 and R is an arbitrary finitely generated associative ring. We also strengthen some of the results on property (T ) for Kac-Moody groups from [DJ].