Pattern matching is a widely used technique in functional languages, especially those in the ML and Haskell traditions. Although pattern matching is typically not built into languages in the Lisp tradition, it is often available via libraries built with macros. We present a sophisticated pattern matcher for Racket, which extends the language using macros, supports novel and widelyuseful pattern...

The focus of this paper is on Ahlfors Q-regular compact sets $$E\subset \mathbb {R}^n$$ such that, for each $$Q-2<\alpha \le 0$$ , the weighted measure $$\mu _{\alpha }$$ given by integrating density $$\omega (x)=\text {dist}(x, E)^\alpha $$ yields a Muckenhoupt $$\mathcal {A}_p$$ -weight in ball B containing E. For E we show existence bounded linear trace operator acting from $$W^{1,p}(B,...

Let $$\mathcal {H}$$ be a complex Hilbert space with inner product $$\langle \cdot , \rangle $$ and let A non-zero bounded positive linear operator on {H}.$$ $$\mathbb {B}_A(\mathcal {H})$$ denote the algebra of all operators which admit A-adjoint, $$N_A(\cdot )$$ seminorm . The generalized A-numerical radius $$T\in \mathbb is defined as $$\begin{aligned} \omega _{N_A}(T)=\displaystyle {\sup _{...

objective: the aim of this study was to assess and compare the effect of two neurofeedback protocols (smr/theta and beta/theta) on adhd symptoms, selective attention and eeg (electroencephalogram) parameters in children with adhd. method: the sample consisted of 16 children (9-15 year old: 13 boys; 3 girls) with adhd-combined type (adhd-c). all of children used methylphenidate (mph) during the ...

For a quasiregular mapping $$f:{\mathbb {R}}^n \rightarrow {\mathbb {R}}^n$$ , with $$n\ge 2$$ Julia limiting direction $$\theta \in S^{n-1}$$ arises from sequence $$(x_n)_{n=1}^{\infty }$$ contained in the set of f, $$|x_n| \infty $$ and $$x_n/|x_n| \theta . directions have been extensively studied for entire meromorphic functions plane. In this paper, we focus on higher dimensions. First...

The spectrum of a graph is closely related to many parameters. In particular, the spectral gap regular which difference between its valency and second eigenvalue, widely seen an algebraic measure connectivity plays key role in theory expander graphs. this paper, we extend previous work done for graphs bipartite present linear programming method obtaining upper bound on order uniform hypergraph ...

We investigate here the following weighted degenerate elliptic system $$\begin{aligned} &-\Delta _{s} u =\Big(1+\|\mathbf{x}\|^{2(s+1)}\Big)^{ \frac{\alpha }{2(s+1)}} v^{p}, \quad -\Delta v= \Big(1+\| \mathbf{x}\|^{2(s+1)}\Big)^{\frac{\alpha }{2(s+1)}}u^{\theta }, \\ &\quad u,v>0 \mbox{in }\; \mathbb{R}^{N}:=\mathbb{R}^{N_{1}}\times \mathbb{R}^{N_{2}}, \end{aligned}$$ where $\Delta _{s}=\Delta ...