Abstract Current nonlinear optical (NLO) materials encounter a classic dilemma in balancing the band gap and birefringence, particularly short wavelength (λ PM ≤ 266 nm) region. Utilizing both π‐conjugated non‐π‐conjugated units to construct NLO crystals has emerged as premier choice nowadays. Herein, combination of [CO 3 ]/[C(NH 2 ) ] moieties phosphorus‐based tetrahedra generates nine new crystals, whose birefringence obtains significant gain compared phosphate crystals. Experimental...

Intracranial atherosclerotic stenosis (ICAS) is a leading cause of failed mechanical thrombectomy (MT). To achieve successful recanalisation, rescue strategies such as balloon angioplasty and stenting are frequently employed. In this study, we aimed to investigate the comparative efficacy safety these strategies. We retrospectively analysed data 321 patients with ICAS-related large vessel occlusion (LVO) treated (n=212) or (n=109) after MT. The primary outcome was favourable outcomes...

The first author conjectured that Chebyshev-type prime bounds hold for Beurling generalized numbers provided the counting function $N(x)$ of integers satisfies $L^1$ condition \[ \int _1^\infty |N(x) - Ax|\,dx/x^2 < \infty \]

In classical prime number theory, several relations are considered to be equivalent the Prime Number Theorem. For Beurling generalized numbers, some auxiliary conditions may needed deduce one relation from another one. We show under which analog of sharp version Mertens' sum formula does or not hold.

Abstract Objective . Electroencephalography (EEG) is an important kind of bioelectric signal for measuring physiological activities the brain, and motor imagery (MI) EEG has significant clinical application prospects. Convolutional neural network become a mainstream algorithm MI classification, however lack subject-specific data considerably restricts its decoding accuracy generalization performance. To address this challenge, novel transfer learning (TL) framework using auxiliary dataset to...

Owing to the tendency form glass state in growing crystals ternary tin(II) borate system, hitherto, very few single were reported. In this paper, a crystal of Sn3B8O15 was obtained via high temperature solution method closed system. The structure features flexible fundamental building block [B8O18]12– constructed by one [BO3]3– unit and [B7O16]11– group that contains three hexatomic rings, which further connect compose two-dimensional 2∞[B8O15] layer structure. connection mode flexibility...

with constants A > 0, q 1, and 0 < v that the generating function Z#(y) in (1 1).Let of ((n) has no zeros on circle [y[ qor assume P (n) be total number primes degree n G.The theorems state 13(n) q"/n + O(qOn) as -where or, equivalently, /(n) := E O(p) r(r) qn O(qOn).pEP,r> rln O(pr)=nIn 12], elementary proofs abstract prime theorem are given.Also, 11 ], subject to weak condition G(n) Aq O(qnn -y)

IntroductionIn 1968 Halhsz [6] proved the following important result: THEOREM.Let f ( n ) be a completely multiplicative function such that If(n)l < 1 holds for all N. Suppose ()n<x This theorem is generalized here in Theorem 1.1 to Beurling's integers [1], [2].We then apply prove 2.1 which generalization of Halsz-Wirsing's [4], [9].From 2.1, we deduce 2.3 on estimate M(x) o(x).The latter combined with Beurling [2] and an example Diamond [3] shows prime number o(x) are not equivalent.1.A...

We introduce the classical theory of interplay between group and topology into context operads explore some applications to homotopy theory. first propose a notion operad then develop operads, extending theories groups, spaces with actions covering classifying groups. In particular, fundamental groups topological is naturally its higher are operad, $K(\pi,1)$ characterized by can be reconstructed from operad. Two most important examples symmetric braid which provide models for...

In this study, we propose a novel approach to sound event localization and detection (SELD) by using separation (SS) models tackle key challenges of high percentage overlapped segments between events imbalanced distributions classes in real-world scenarios. Specifically, introduce class-dependent SS deal with overlapping mixtures extract features from the model as prompts for SELD specific class. The proposed SS-SELD method enhances overall performance system, resulting improved accuracy...

Borophosphates have become promising candidates for ultraviolet or deep-ultraviolet functional crystals. Through high-temperature solution method, four new borophosphates, K2B2P2O9, (NH4)2BP2O7(OH), K2BP2O7(OH), and P21/c-(NH4)2B2P3O11(OH), were acquired successfully. Single crystal X-ray diffraction suggests that K2BP2O7(OH) belong to the noncentrosymmetric space group, while P21/c-(NH4)2B2P3O11(OH) belongs centrosymmetric compound. It is worth mentioning present fundamental building blocks...

Elementary proofs of the abstract prime number theorem form <inline-formula content-type="math/mathml"> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="normal upper Lamda left-parenthesis m right-parenthesis equals q Superscript Baseline plus O negative 1 right-parenthesis"> <mml:semantics> <mml:mrow> <mml:mi mathvariant="normal">Λ<!-- Λ --></mml:mi> <mml:mo stretchy="false">(</mml:mo> <mml:mi>m</mml:mi> stretchy="false">)</mml:mo> <mml:mo>=</mml:mo> <mml:mrow...

Halász’s mean-value theorem is well-known and important in classical probabilistic number theory. It generalized to Beurling numbers as follows. Let $f(n_i)$ be a completely multiplicative function on numbe

A function $f(x)$ defined on $[a,\infty)$, $a\ge 0$, is said to be linearly slowly decreasing with index $\alpha \ge 0$ if \[ \liminf_{x\to \infty,\, y/x\to 1+} (x\log^\alpha x)^{-1}(f(y)-f(x))\ge 0. \] Nondecreasing functions and fu

We establish certain smash operations on spaces over operads which are general analogues of the Samelson product single loop spaces, and obtain a conceptual description structure homotopy groups $Y$ symmetric $K(\pi,1)$ operad: $\pi_*Y$ is module free algebraic operad generated by induced these operations. In particular double conjugacy classes Brunnian braids modulo conjugation action pure braids.