The object people perceive in an image can depend on its orientation relative to the scene it is in (its reference frame). For example, the images of the symbols × and + differ by a 45 degree rotation. Although real scenes have multiple images and reference frames, psychologists have focused on scenes with only one reference frame. We propose an ideal observer model based on nonparametric Bayes...

Abstract Here, the existence and multiplicity of weak solutions to a generalized $(p(\cdot ),q(\cdot ))$ ( p ⋅ ) , q -Laplace equation involving Leray–Lions type operators with Hardy potential are studied under Dirichlet boun...

The estimate of the change rate solar gravitational parameter $\mathrm{d}(GM_{\odot})/\mathrm{d}t$ is obtained from processing modern positional observations planets and spacecraft. Observations were processed parameters determined basing on numerical planetary ephemeris EPM2019. annual decrease in mass $M_{\odot}$ accounts for loss through radiation ${\dot M}_{{\odot}\mathrm{rad}}$, outgoing w...

Given two sets of natural numbers $\mathcal{A}$ and $\mathcal{B}$ density $1$ we prove that their product set $\mathcal{A}\cdot \mathcal{B}:=\{ab:a\in\mathcal{A},\,b\in\mathcal{B}\}$ also has $1$. On the other hand, for any $\varepsilon>0$, show there are $>1-\varepsilon$ which $\mathcal{A}\cdot\mathcal{A}$ $<\varepsilon$. This answers questions Hegyv\'{a}ri, Hennecart Pach.

The orientation morphism $Or(\cdot)(P)\colon \gamma\mapsto\dot{P}$ associates differential-polynomial flows $\dot{P}=Q(P)$ on spaces of bi-vectors $P$ finite-dimensional affine manifolds $N^d$ with (sums of) finite unoriented graphs $\gamma$ ordered sets edges and without multiple one-cycles. It is known that $d$-cocycles $\boldsymbol{\gamma}\in\ker d$ respect to the vertex-expanding differenti...

the main objective of this study is to swing krull intersection theorem in primary decomposition of rings and modules to the primary decomposition of soft rings and soft modules. to fulfill this aim several notions like soft prime ideals, soft maximal ideals, soft primary ideals, and soft radical ideals are introduced for a soft ring over a given unitary commutative ring. consequently, the p...

let r be a commutative ring with identity. let n and k be two submodules of a multiplication r-module m. thenn=im and k=jm for some ideals i and j of r. the product of n and k denoted by nk is defined by nk=ijm. inthis paper we characterize some particular cases of multiplication modules by using the product of submodules.

New explicit exponential stability conditions are presented for the non-autonomous scalar linear functional differential equation $$ \dot{x}(t) + \sum_{k=1}^m a_k(t)x(h_k(t)) \int_{g(t)}^t K(t,s) x(s)ds=0, where $h_k(t)\leq t$, $g(t)\leq $a_k(\cdot)$ and kernel $K(\cdot,\cdot)$ oscillatory and, generally, discontinuous functions. The proofs based on establishing boundedness of solutions later u...

Symmetry in neutrino oscillation serves for a better understanding of the physical properties phenomenon. We present systematic way finding symmetry oscillation, which we call Finder (SF). By extending known framework vacuum into matter environment, derive SF equation, powerful machinery identifying system. After learning lessons on Zaglauer-Schwarzer system with equivalent symmetry, apply meth...

In this paper we give some general results on the non-splitextension group $overline{G}_{n} = 2^{2n}{^{cdot}}Sp(2n,2), ngeq2.$ We then focus on the group $overline{G}_{4} =2^{8}{^{cdot}}Sp(8,2).$ We construct $overline{G}_{4}$ as apermutation group acting on 512 points. The conjugacy classes aredetermined using the coset analysis technique. Then we determine theinertia factor groups and Fischer...