In this article, we introduce the concept of weak F?m,?-contractions on relation-theoretic m-metric spaces and establish related fixed point theorems, where ? is a control function ? relation. Then, detail some results for cyclic-type F?m,?-contraction mappings. Finally, demonstrate illustrative examples discuss upper lower solutions Volterra-type integral equations form ??=?0?A?,?,??m?+??,??0,1.

An embedded-domain phase-field formalism is used for studying phase transformation pathways in bimetallic nanoparticles (BNPs). Competition of bulk and surface-directed spinodal decomposition processes their interplay with capillarity are identified as the main determinants BNP morphology. The former characterized by an effective driving force $\Delta\tilde{f}$ which increases decreasing temper...

Introduction: Research evidence indicates that maladaptive reorganization of the brain plays a critical role in amplifying pain experiences and pain chronification; there is, however, no clear evidence of change in brain wave activity among patients with chronic low back pain (CLBP). The objective of this study was to assess brain wave activity in patients with CLBP, compared to healthy control...

We consider a special theta lift $\theta(f)$ from cuspidal Siegel modular forms $f$ on $\mathrm{Sp}_4$ to "modular forms" $\mathrm{SO}(4,4)$. This can be considered an analogue of the Saito-Kurokawa lift, where now image is representations $\mathrm{SO}(4,4)$ that are quaternionic at infinity. relate Fourier coefficients those $f$, and in particular prove nonzero has algebraic if does. Restricti...

The idea of difference sequences of real (or complex) numbers was introducedby Ki zmaz cite{Kizmaz}. In this paper, using the difference operator and alacunary sequence, we introduce and examine the class of sequence $bv_{theta}left(  Delta,mathcal{F}right)  .$ We study some of its properties likesolidity, symmetricity, etc.

We prove a conjecture of Teissier asserting that if $f$ has an isolated singularity at $P$ and $H$ is smooth hypersurface through $P$, then $\widetilde{\alpha}\_P(f)\geq \widetilde{\alpha}\_P(f\vert\_H)+\frac{1}{\theta\_P(f)+1}$, where $\widetilde{\alpha}\_P(f)$ $\widetilde{\alpha}\_P(f\vert\_H)$ are the minimal exponents $f\vert\_H$, respectively, $\theta\_P(f)$ invariant obtained by comparing...

We monitored the radial distribution of sap flux density (v; g H2O m(-2) s(-1)) in the sapwood of six plantation-grown Pinus taeda L. trees during wet and dry soil periods. Mean basal diameter of the 32-year-old trees was 33.3 cm. For all trees, the radial distribution of sap flow in the base of the stem (i.e., radial profile) was Gaussian in shape. Sap flow occurred maximally in the outer 4 cm...

This article deals with studies that monitor occurrences of a recurrent event for n subjects or experimental units. It is assumed that the i(th) unit is monitored over a random period [0,tau(i)]. The successive inter-event times T(i1), T(i2), ..., are assumed independent of tau(i). The random number of event occurrences over the monitoring period is K(i) = max{k in {0, 1, 2, ...} : T(i1) + T(i2...

In the present paper, two theorems are discussed, one is fixed point theorem and another \(n\)-tuple for a new contractive condition in bi-complete $F$-quasi metric space. Also, an example given to validate result.

We present a maximal $$L_{q}(L_{p})$$ -regularity theory with Muckenhoupt weights for the equation 0.1 $$\begin{aligned} \partial ^{\alpha }_{t}u(t,x)=a^{ij}(t,x)u_{x^{i}x^{j}}(t,x)+f(t,x),\quad t>0,x\in {\mathbb {R}}^{d}. \end{aligned}$$ Here, $$\partial }_{t}$$ is Caputo fractional derivative of order $$\alpha \in (0,2)$$ and $$a^{ij}$$ are functions (t, x). Precisely, we show that \begin{ali...