Related papers: About solving the Fechner-Stevens problem
In this paper we are concerned with the solutions of the differential equation $f'''+ff''+g(f')=0$ on $[0,\infty)$, satisfying the boundary conditions $f(0)=\alpha$, $f'(0)=\beta\geq 0$, $f'(\infty)=\l$, and where $g$ is some given…
In this paper, we establish some Fleck-Weisman type and Davis-Sun type congruences for the Stirling numbers and the Eulerian numbers.
We answer a question of Pakhomov by showing that there is a consistent, c.e. theory $T$ such that no theory which is definitionally equivalent to $T$ has a computable model. A key tool in our proof is the model-theoretic notion of mutual…
Justification theory is an abstract unifying formalism that captures semantics of various non-monotonic logics. One intriguing problem that has received significant attention is the consistency problem: under which conditions are…
A novel approach to an old symmetry problem is developed. A new proof is given for the following symmetry problem, studied earlier.
We develop a geometric framework that unifies several different combinatorial fixed-point theorems related to Tucker's lemma and Sperner's lemma, showing them to be different geometric manifestations of the same topological phenomena. In…
If $X$ is a finite tree and $f \colon X \longrightarrow X$ is a map, as the Main Theorem of this paper we find eight conditions, each of which is equivalent to the fact that $f$ is equicontinuous. To name just a few of the results obtained:…
We show that Pinney's equation [2] with a constant coefficient can be reduced to its linear part by a simple change of variables. Also, Pinney's original solution is simplified slightly.
We survey the various constructions of forward self-similar solutions (and generalizations of self-similar solutions) to the Navier-Stokes equations. We also include and prove an extension of a recent result from [7].
In this paper we consider the model of phase relaxation introduced in [22], where an asymptotic analysis is performed toward an integral formulation of the Stefan problem when the relaxation parameter approaches zero. Assuming the natural…
In this paper, we prove that the induced representation theories of two equivalent Fell bundles are essentially identical; and we apply our results to carry the induced representation theory and imprimitivity theorems of saturated Fell…
We discuss equivalence conditions on the non-existence of non-trivial meromorphic solution to the Fermat Diophantine equations $f^m(z)+g^n(z)=1$ with integers $m,n\geq2$, from which other approaches to prove little Picard theorem are…
In this paper, we study the behaviour of TF-isomorphisms, a natural generalisation of isomorphisms. TF-isomorphisms allow us to simplify the approach to seemingly unrelated problems. In particular, we mention the Neighbourhood…
We expose the most advanced equiconvergence results for Birkhoff- and Stone-regular differential operators and present also author's approach to this problem. We give a full proof of equiconvergence on the whole interval, which constitutes…
A second order finite-difference equation has two linearly independent solutions. It is shown here that, like in the continuous case, at most one of the two can be a polynomial solution. The uniqueness in the classical continuous…
There are a number of experiments and observations that appear to argue for the existence of particles, including the photoelectric and Compton effects, exposure of only one film grain by a spread-out photon wave function, and particle-like…
We investigate whether or not an Einstein Static universe is a solution to the cosmological equations in $f(R)$ gravity. It is found that only one class of $f(R)$ theories admits an Einstein Static model, and that this class is neutrally…
We present a direct confirmation of the validity of the equivalence principle for unstructured test bodies in scalar tensor gravity. Our analysis is complementary to previous approaches and valid for a large class of scalar-tensor theories…
In this work we mainly prove the existence and pathwise uniqueness of solutions to general backward doubly stochastic differential equations with jumps appearing in both forward and backward integral parts. Several comparison theorems under…
In this paper, we have considered second order non-homogeneous linear differential equations having entire coefficients. We have established conditions ensuring non-existence of finite order solution of such type of differential equations.