In this paper we study, via variational methods, the problem of scattering of time harmonic acoustic waves by an unbounded sound soft surface. The boundary ∂D is assumed to lie within a finite distance of a flat plane and the incident wave is that arising from an inhomogeneous term in the Helmholtz equation whose support lies within some finite distance of the boundary ∂D. Via analysis of an eq...

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.

We prove existence of infinite volume Gibbs measures relative to Brownian motion. We require the pair potential W to fulfill a uniform integrability condition, but otherwise our restrictions on the potentials are relatively weak. In particular, our results are applicable to the massless Nelson model. We also prove an upper bound for path fluctuations under the infinite volume Gibbs measures.

In this paper we introduce and study enhanced notions of relative Pareto minimizers to constrained multiobjective problems that are defined via several kinds of relative interiors of ordering cones and occupy intermediate positions between the classical notions of Pareto and weak Pareto efficiency /minimality. Using advanced tools of variational analysis and generalized differentiation, we esta...

The existence of a natural and projectively equivariant quantization in the sense of Lecomte [20] was proved recently by M. Bordemann [4], using the framework of Thomas-Whitehead connections. We give a new proof of existence using the notion of Cartan projective connections and we obtain an explicit formula in terms of these connections. Our method yields the existence of a projectively equivar...

Mabuchi solitons generalize Kähler–Einstein metrics on Fano manifolds, which constitute a Yau–Tian–Donaldson type correspondence with relative Ding stability. Comparing Kähler–Ricci solitons, there is distinct necessary condition for the existence. We show this can be implied by uniformly For this, we study inner product of $$\mathbb {C}^{*}$$ -actions equivariant test-configurations and obtain...

The SIMP approach is one of the most frequently used methods for topology optimization of structures. In this method, the relative density is expressed as a function of coordinates and varies from 0 to 1 within the design domain. Relative densities of 0 and 1 are associated to the existence and non-existence of the material, respectively. The finite element approach is usually utilized to analy...

according to heidegger human existence is not encapsulated and limited in itself, rather it is a transcendental existence which is standing out in the world. this ecstasy is rooted in the deeper relation between human existence and being. in heidegger philosophy this necessary relation between man and world is an essential element in the existential structure of man. that is why he uses the ter...