let $p$ be a prime number greater than three. in this paper, we prove the existence of a new family of homotopy elements in the stable homotopy groups of spheres $pi_{ast}(s)$ which is represented by $h_nh_mtilde{beta}_{s+2}in {rm ext}_a^{s+4, q[p^n+p^m+(s+2)p+(s+1)]+s}(mathbb{z}_p,mathbb{z}_p)$ up to nonzero scalar in the adams spectral sequence, where $ngeq m+2>5$, $0leq sext}_a^{s+2,q[(s+2)p...

In this paper, the problem under consideration is multiobjective non-linear fractional programming problem involving semilocally convex and related functions. We have discussed the interrelation between the solution sets involving properly efficient solutions of multiobjective fractional programming and corresponding scalar fractional programming problem. Necessary and sufficient optimality...

The spontaneous scalarization during the stellar core collapse in massive scalar-tensor theories of gravity introduces extra polarizations (on top plus and cross modes) gravitational waves, whose amplitudes are determined by several model parameters. Observations such scalarization-induced waveforms therefore offer valuable probes into these gravity. Considering a triple-scalar interactions the...

We study scalar perturbations induced by through the non-linear interaction appearing at second order in perturbations. derive analytic solutions of a perfect fluid. In particular, we consider radiation-dominated era and matter-dominated era. With solutions, also discuss power spectra

We introduce the notion of scalar fuzzy McShane and Henstock integrals for number valued functions we discuss their relationship give a version Gordon theorem [24].

FIXME Automatic differentiation tools use 1 of 2 strategies to access derivative values. These strategies are: 1. By-address 2. By-name The by-address method is typically implemented by introducing structured types for each active scalar type. For example, scalar type ’real’ will have an associated structure type ’active-real’. Using this strategy, all active variables types are changed to the ...

A tight lower bound for required I/O when computing a matrix-matrix multiplication on a processor with two layers of memory is established. Prior work obtained weaker lower bounds by reasoning about the number of phases needed to perform C := AB, where each phase is a series of operations involving S reads and writes to and from fast memory, and S is the size of fast memory. A lower bound on th...