Edge proximity and matching extension in projective planar graphs

A graph $G$ with at least $2m+2$ vertices is said to be distance $d$ $m$-extendable if, for any matching $M$ of $G$ with $m$ edges in which the edges lie at distance at least $d$ pairwise, there exists a perfect matching of $G$ containing $M$. In this paper we prove that every 5-connected triangulation on the projective plane of even order is distance 3 7-extendable and distance 4 $m$-extendable for any $m$.     

Gorenstein平坦模与Frobenius扩张

设R■A是环的Frobenius扩张,其中A是右凝聚环,M是任意左A-模.首先证明了_AM是Gorenstein平坦模当且仅当M作为左R-模也是Gorenstein平坦模.其次,证明了Nakayama和Tsuzuku关于平坦维数沿着Frobenius扩张的传递性定理的"Gorenstein版本":若_AM具有有限Gorenstein平坦维数,则Gfd_A(M)=Gfd_R(M).此外,证明了若R■S是可分Frobenius扩张,则任意A-模(不一定具有有限Gorenstein平坦维数),其Gorenstein平坦维数沿着该环扩张是不变的.     

The trigonometric triangle

A procedure is presented by which the integration of a function such as cos ⁿ (x) or sin ⁿ (x) with n = 1, 2, 3, 4 … is facilitated.     

Measure and integration: The basic extension and representation theorems in terms of new inner and outer envelopes

The work of the author in measure and integration is based on new inner and outer envelope formations, which replace the traditional Carathéodory outer measure and certain simple suprema and infima. The new formations lead to essential improvements in both the extent and the adequacy of the basic results. However, they did not find an entrance into the recent textbook literature. The present paper seeks to demonstrate their power with the examples of the basic inner and outer extension and representation theorems for set functions and functionals.     

Construction of Multivariate Tight Framelet Packets Associated with Dilation Matrix

In this paper, we present a method for constructing multivariate tight framelet packets associated with an arbitrary dilation matrix using unitary extension principles.We also prove how to construct various tight frames for L2(Rd) by replac-ing some mother framelets.     

扩张环上的$\Sigma$-相伴素理想

作为对相伴素理想与幂零相伴素理想的推广,我们在本文中引进了$\Sigma$-相伴素理想的定义,探讨了$\Sigma$-相伴素理想的基本性质,证明了Ore扩张环$R[x;\alpha,\delta]$、斜洛朗多项式环$R[x,x^{-1};\alpha]$及斜幂级数环$R[[x;\alpha]]$的$\Sigma$-相伴素理想都分别可以用环$R$的$\Sigma$-相伴素理想来刻画,从而将相伴素理想与幂零相伴素理想的一些已有结论推广到更一般的情形.     

半格分次弱Hopf代数的$G$-Cleft扩张

本文首先将Clifford幺半群代数分解为交叉积的半格直和,然后将这个结果通过$H$-$G$-cleft扩张推广到所谓的$G$-交叉积上.     

Synthesis and characterization of biodegradable polyesteramides constructed mainly by alternating diesterdiamide units from N,N′-bis(2-hydroxyethyl)-adipamide and diacids

Two kinds of aliphatic alternating polyesteramide prepolymers were prepared through melt polycondensation from N,N’-bis(2-hydroxyethyl)-adipamide and adipic acid or sebacic acid. Chain extension of them was conducted with 2,2′-(1,4-phenylene)-bis(2-oxazoline) and adipoyl biscaprolactamate as combined chain extenders. The chain extended polyesteramides (ExtPEAs) were characterized by IR, 1 H-NMR, differential scanning calorimetry, thermogravimetric analysis, wide angle X-ray scattering, tensile test and enzymatic degradation. The results showed that the ExtPEA(4,m)s were mainly constituted with the diester adipamide alternating units. ExtPEA(4,4) and ExtPEA(4,8) had Tm of 83.8℃ and 85.8℃ and initial decomposition temperature above 310.0℃. They crystallized similarly as Nylon-66 did and were flexible thermoplastic materials with tensile strength up to 25.64 MPa and strain at break up to 737%.     

The isometric extension problem between unit spheres of two separable Banach spaces

In this article, we use some analytic and geometric characters of the smooth points in a sphere to study the isometric extension problem in the separable or reflexive real Banach spaces. We obtain that under some condition the answer to this problem is affirmative.     

Effect of training level and blood flow restriction on thermal parameters: Preliminary study

Training with blood flow restriction could lead to an effect on skin temperature. Additionally, this effect could be higher in people with lower physical fitness level due to their lower capacity of heat loss. The aim of this preliminary study was therefore to evaluate the effects of training experience on the acute and chronic thermal skin responses after performing exercise with and without blood flow restriction. The study included ten men, of these, five were trained. All subjects performed tests and re-tests for maximum strength (1 repetition maximum) through unilateral leg extensions (right thigh at 45 ± 6.7 kg and left thigh at 45.5 ± 8.1 kg, p > 0.05). The protocol consisted of four sets to concentric failure, with one-minute rest intervals between sets at an intensity corresponding to 40% of 1 RM. There were 7-day intervals between experimental sessions (150 mmHg versus unrestricted flow restriction). The thermal images were made before the protocol (pre), immediately after the end of the series (post), and 24 h afterward (post 24 h). When comparing temperature variation (Δ exercise and Δ 24 h) between groups, it was observed that the trained participants showed a greater drop in temperature 24 h after exercise with 150 mmHg restriction (confidence interval: 95% of Δ 24 h [−0.2 to −0.9 °C]) compared to untrained subjects (p = 0.006 and ES > 1.5, confidence interval: 95% Δ 24 h [−0.1 to 0.6 °C].) In conclusion, this preliminary study showed that training experience interferes with the chronic cutaneous thermal temperature of the anterior thigh when strength training associated with blood flow restriction 150 mmHg was performed.