热毛细对流的液桥几何位形及浮力效应

本文讨论重力对不同高度、直径比液桥的热毛细对流的影响。当液桥高度、直径比增大时,液桥中的等流函数线呈双涡结构,这种流动图样并不必然与热毛细振荡流相联系。在地面热毛细对流实验中模拟空间微重力情况,液桥高度需小于1.5mm。在微重力环境中,液桥内的流场和温度分布介于地面相同参数液桥的上部加热和下部加热两种结果之间。因此,可以用地面实验结果估计空间液桥的对流和热输运情况。     

Gaps in the number of generators of monomial Togliatti systems

Let $I_{d,n}?k[x_0,?,x_n]$ be a minimal monomial Togliatti system of forms of degree d. In [4], Mezzetti and Miró-Roig proved that the minimal number of generators $\mu (I_{d,n})$ of $I_{d,n}$ lies in the interval $[2n+1,\left(\begin{array}{c}n+d?1\\ n?1\end{array}\right)]$. In this paper, we prove that for $n\ge 4$ and $d\ge 3$, the integer values in $[2n+3,3n?1]$ cannot be realized as the number of minimal generators of a minimal monomial Togliatti system. We classify minimal monomial Togliatti systems $I_{d,n}?k[x_0,?,x_n]$ of forms of degree d with $\mu (I_{d,n})=2n+2$ or 3n (i.e. with the minimal number of generators reaching the border of the non-existence interval). Finally, we prove that for $n=4$, $d\ge 3$ and $\mu \in [9,\left(\begin{array}{c}d+3\\ 3\end{array}\right)]?\{11\}$ there exists a minimal monomial Togliatti system $I_{d,n}?k[x_0,?,x_n]$ of forms of degree d with $\mu (I_{n,d})=\mu$.     

Bounded sets structure of CpX and quasi‐(DF)‐spaces

For wide classes of locally convex spaces, in particular, for the space $C_p(X)$ of continuous real‐valued functions on a Tychonoff space X equipped with the pointwise topology, we characterize the existence of a fundamental bounded resolution (i.e., an increasing family of bounded sets indexed by the irrationals which swallows the bounded sets). These facts together with some results from Grothendieck's theory of $(DF)$‐spaces have led us to introduce quasi‐ $(DF)$‐spaces, a class of locally convex spaces containing $(DF)$‐spaces that preserves subspaces, countable direct sums and countable products. Regular $(LM)$‐spaces as well as their strong duals are quasi‐ $(DF)$‐spaces. Hence the space of distributions $D^{\prime }(\mathrm{\Omega })$ provides a concrete example of a quasi‐ $(DF)$‐space not being a $(DF)$‐space. We show that $C_p(X)$ has a fundamental bounded resolution if and only if $C_p(X)$ is a quasi‐ $(DF)$‐space if and only if the strong dual of $C_p(X)$ is a quasi‐ $(DF)$‐space if and only if X is countable. If X is metrizable, then $C_k(X)$ is a quasi‐ $(DF)$‐space if and only if X is a σ‐compact Polish space.     

A layer potential analysis for transmission problems for Brinkman‐type systems in Lipschitz domains in

The aim of this paper is to establish a well‐posedness result for a boundary value problem of transmission‐type for the standard and generalized Brinkman systems in two Lipschitz domains in , the former being bounded, and the latter, its complement in . As a first step, we establish a well‐posedness result for a transmission problem for the standard Brinkman systems on complementary Lipschitz domains in by making use of the Potential theory developed for such a system. As a second step, we prove our desired result (in L²‐based Sobolev spaces) by using a method based on Fredholm operator theory and the well‐posedness result from the previous step.     

Dayaolingzhiols A−E,AchE inhibitory meroterpenoids from Ganoderma lucidum

Ganoderma mushrooms are widely used as effective medicines for treating and preventing chronic diseases. In this study, five new meroterpenoids, dayaolingzhiols A (1) and B (2) featuring a 6/6/6 ring system, dayaolingzhiols C?E (3–5) harboring a γ-lactone motif, along with eight known ones (6–13), were purified from G. lucidum. To clarify their chemical structures, spectroscopic and ECD and OR computational methods were used. In addition, the inhibition of all the new meroterpenoids against AChE was evaluated, disclosing that (+)-4 and (±)-5 possess potent AChE inhibitory activities with respective IC₅₀ values of 8.52?±?1.90?μM and 7.37?±?0.52?μM.     

Controllability results for the Moore–Gibson–Thompson equation arising in nonlinear acoustics

We show that the Moore–Gibson–Thomson equation

$\tau {?}_{ttt}y+\alpha {?}_{tt}y?c^2\mathrm{\Delta }y?b\mathrm{\Delta }{?}_{t}y=k{?}_{tt}(y^2)+{\chi }_{\omega (t)}u,$

is controlled by a force that is supported on an moving subset $\omega (t)$ of the domain, satisfying a geometrical condition. Using the concept of approximately outer invertible map, a generalized implicit function theorem and assuming that $\gamma :=\alpha ?\frac{\tau c^2}{b}>0$, the local null controllability in the nonlinear case is established. Moreover, the analysis of the critical value $\gamma =0$ for the linear equation is included.     

The structure of DGA resolutions of monomial ideals

Let $I?\mathbb{k}[x_1,\dots ,x_n]$ be a squarefree monomial ideal in a polynomial ring. In this paper we study multiplications on the minimal free resolution $\mathbb{F}$ of $\mathbb{k}[x_1,\dots ,x_n]/I$. In particular, we characterize the possible vectors of total Betti numbers for such ideals which admit a differential graded algebra (DGA) structure on $\mathbb{F}$. We also show that under these assumptions the maximal shifts of the graded Betti numbers are subadditive.On the other hand, we present an example of a strongly generic monomial ideal which does not admit a DGA structure on its minimal free resolution. In particular, this demonstrates that the Hull resolution and the Lyubeznik resolution do not admit DGA structures in general.Finally, we show that it is enough to modify the last map of $\mathbb{F}$ to ensure that it admits the structure of a DG algebra.     

Photooptical Properties of Polymethacrylates Having Cyanoazobenzene‐Containing Side Groups with Lateral Methyl Substituents and Different Spacer Length

New photochromic polymethacrylates with different spacer length having azobenzene side groups and lateral methyl substituents were synthesized. The phase behavior of polymethacrylates and their photooptical properties were studied and compared with unsubstituted analogues. It is shown that an introduction of lateral methyl substituents results in almost complete suppression of liquid crystalline (LC) phase formation and strong decrease of photoinduced dichroism values. It is found that rates of the photoinduced E‐Z isomerization and back thermal Z‐E isomerization are almost independent on spacer lengths. Due to the presence of lateral substituents, the photoinduced azobenzene Z‐form shows remarkable long lifetime, and back thermal conversion at room temperature takes more than 10 days. Specific peculiarities of the photoorientation process in polymer films under the polarized UV and visible light action were studied and their mechanism is suggested. © 2019 Wiley Periodicals, Inc. J. Polym. Sci., Part B: Polym. Phys. 2019 , 57, 1337–1342     

Two-dimensional vortex sheets for the nonisentropic Euler equations: Nonlinear stability

We show the short-time existence and nonlinear stability of vortex sheets for the nonisentropic compressible Euler equations in two spatial dimensions, based on the weakly linear stability result of Morando and Trebeschi (2008) [20]. The missing normal derivatives are compensated through the equations of the linearized vorticity and entropy when deriving higher-order energy estimates. The proof of the resolution for this nonlinear problem follows from certain a priori tame estimates on the effective linear problem in the usual Sobolev spaces and a suitable Nash–Moser iteration scheme.