We study momentum dependence of static magnetic susceptibility $\chi(q)$ in paramagnetic phase Heisenberg magnets and its relation to critical behavior within nonlinear sigma model (NLSM) at arbitrary dimension $2<d<4$. In the first order $1/N$ expansion, where $N$ is number spin components, we find $\chi(q)\propto[q^{2}+\xi^{-2}(1+f(q\xi ))]^{-1+\eta /2}$, $\xi $ correlation length, $q$ moment...

For positive rank r elliptic curves E(Q), we employ ideal class pairingsE(Q)×E−D(Q)→CL(−D), for quadratic twists E−D(Q) with a suitable “small y-height” rational point, to obtain explicit number lower bounds that improve on earlier work by the authors. E(a):y2=x3−a, r(a), this givesh(−D)≥110⋅|Etor(Q)|RQ(E)⋅πr(a)22r(a)Γ(r(a)2+1)⋅log⁡(D)r(a)2log⁡log⁡D, representing general improvement classical b...

We define a discrete version of the bilinear spherical maximal function, and show $$l^{p}(\mathbb {Z}^d)\times l^{q}(\mathbb {Z}^d) \rightarrow l^{r}(\mathbb {Z}^d)$$ bounds for $$d \ge 3$$ , $$\frac{1}{p} + \frac{1}{q} \frac{1}{r}$$ $$r>\frac{d}{d-2}$$ $$p,q\ge 1$$ . Due to interpolation, key estimate is an l^{\infty }(\mathbb l^{p}(\mathbb bound, which holds when $$p>\frac{d}{d-2}$$ A feature...

Abstract Analogously to primes in arithmetic progressions large moduli, we can study that are totally split extensions of ${\mathbb {Q}}$ high degree. Motivated by a question Kowalski focus on the {Q}}(E[d])$ obtained adjoining coordinates $d$-torsion points non-CM elliptic curve $E/{\mathbb {Q}}$. We show for almost all integers $d$ there exists and prime $p&amp;lt;|\text {Gal}({\mathbb {Q}}(E...

We evaluated the activity of quinupristin-dalfopristin (Q-D) against three clinical strains of Staphylococcus aureus susceptible to Q (MIC, 8 microg/ml) and Q-D (MICs, 0.5 to 1 microg/ml) but displaying various levels of susceptibility to D. D was active against S. aureus HM 1054 (MIC, 4 microg/ml) and had reduced activity against S. aureus RP 13 and S. aureus N 95 (MICs, 32 and 64 microg/ml, r...

A finite automaton .d with a distance function d is a sextuple, (C, Q, M, S, F, d), such that C is the input alphabet, Q is the finite set of states, M: Q x C -+ 2Q is the transition function, S c Q and F c Q are the sets of initial and final states, respectively, d: Q x C x Q -+ (0, 1, co } is the distance function, where co denotes infinity, and d satisfies the following: for any (q,a,q’)E Q ...

We deene a dyadic counterpart Q d p of Q p , and study some relations between Q p and Q d p. For example, a function on T belongs to Q p if and only if (almost) all its translates belong to Q d p. Conversely, functions in Q p may be obtained by averaging translates of functions in Q d p .

Using the Barrow entropy and considering timescale as IR cutoff, a new holographic dark energy model named agegraphic (BADE) was proposed. We use phase space analysis method to discuss evolution of universe in three different mode BADE (Q=0; Q=3?H(?m+?D); Q=H(??m+??D)). find attractor which represents energy-dominated era exists all cases. In case Q=0 Q=H(??m+??D) with ?=0, can behave cosmologi...