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We propose an efficient strategy based on the electrospinning technique combined with multi-dimensional fillers to fabricate composites with well-established thermal pathways. A bridge-type structure is constructed in the composite fibers by integrating 1D boron nitride nanofibers and 2D boron nitride nanosheets, which can accelerate the formation of a valid thermal network, thereby the BNNS/BNNF/polyacrylonitrile (bsf) composites perform better than the BNNS/polyacrylonitrile (bs) composites. This strategy can be extended to the preparation of other electrospun 1D/2D nanofiller/polymer composite fiber films.

Hexadecyl trimethyl ammonium bromide favors CO2 surface diffusion and inhibits excessive proton accumulation on Zn electrodes.

A partial flag variety P K of a Kac–Moody group G has a natural stratification into projected Richardson varieties. When G is a connected reductive group, a Bruhat atlas for P K was constructed in He et al. (2013): P K is locally modelled with Schubert varieties in some Kac–Moody flag variety as stratified spaces. The existence of Bruhat atlases implies some nice combinatorial and geometric properties on the partial flag varieties and the decomposition into projected Richardson varieties. A Bruhat atlas does not exist for partial flag varieties of an arbitrary Kac–Moody group due to combinatorial and geometric reasons. To overcome obstructions, we introduce the notion of Birkhoff–Bruhat atlas. Instead of the Schubert varieties used in a Bruhat atlas, we use the J -Schubert varieties for a Birkhoff–Bruhat atlas. The notion of the J -Schubert varieties interpolates Birkhoff decomposition and Bruhat decomposition of the full flag variety (of a larger Kac–Moody group). The main result of this paper is the construction of a Birkhoff–Bruhat atlas for any partial flag variety P K of a Kac–Moody group. We also construct a combinatorial atlas for the index set Q K of the projected Richardson varieties in P K . As a consequence, we show that Q K has some nice combinatorial properties. This gives a new proof and generalizes the work of Williams (2007) in the case where the group G is a connected reductive group.

Camellia fascicularis is a unique plant rich in bioactive components. However, the isolation of the active substances in C. fascicularis leaves via sequential extraction with solvents of different polarity and the determination of their antioxidant and antitumor activities have not been reported. In this study, the total methanol extract of C. fascicularis leaves was sequentially extracted with different polar solvents, and the corresponding petroleum ether extract (PEE), ethyl acetate extract (EAE), and water extract (WE) were analyzed for their contents in active substances such as flavonoids, polyphenols, polysaccharides, and saponins. The antioxidant ability of the polar extracts was investigated by determining their reducing power and the radical scavenging rate on 1,1-diphenyl-2-picrylhydrazyl (DPPH), 2,2′-azino-bis (3-ethylbenzothiazoline-6-sulfonic acid) (ABTS), and hydroxyl radicals, and CCK-8 and Annexin-FITC/propidium iodide staining assays were conducted to investigate their inhibitory effects on HCCLM6 and HGC27 tumor cells. The results showed that PEE had a high saponin content of 197.35 ± 16.21 mg OAE/g, while EAE and WE exhibited a relatively higher polysaccharide content of 254.37 ± 1.99 and 373.27 ± 8.67 mg GE/g, respectively. The EAE demonstrated the greatest reducing power and the strongest clearing abilities on ABTS and DPPH radicals with respective EC50 values of 343.45 ± 20.12 and 14.07 ± 0.06 μg/ml. Moreover, the antitumor ability of the different polar extracts was dose-dependent, with WE showing the most potent inhibitory ability against HCCLM6 and HGC27 cells.

Most polymers possess low thermal conductivity and are therefore limited in thermal management applications. A key solution is to develop highly thermally conductive polymer composites by incorpora...

The study of certain union $$X(\mu , b)$$ of affine Deligne–Lusztig varieties in the affine flag varieties arose from the study of Shimura varieties with Iwahori level structure. In this paper, we give an explicit dimension formula for $$X(\mu , b)$$ associated to sufficiently large dominant coweight $$\mu $$ .

Tissue factor (TF) which plays a key role in hemostasis and thrombosis appears to be an attractive target and medicinal plants having alkaloids inhibition TF activity benefit to cardiovascular disease (CVD). The aim of study is to explore further knowledge about alkaloids and TF. TF procoagulant activities were determined by the simplified chromogenic assay and their mRNA expression were then examined by reverse transcription and polymerase chain reaction. Besides, the potential of TF/FVIIa binding with four representative alkaloids were analyzed by molecular docking. The results indicated that these isoquinoline alkaloids with various structures had a different effect on suppression of TF activity. Molecular docking showed four alkaloids including l-corydalmine, berberine, jatrorrhizine, and tetrahydropalmatine were stably posed in the active binding pocket of TF/FVIIa. The SARs analysis showed the structural difference including planar, quaternary nitrogen, and the peripheral functional groups at C-8, C-9, C-10, have strong effect on inhibition of TF activity, which provided effective methods to modify isoquinoline alkaloids for inhibiting TF activity. This study provides a further evidence for the cardiovascular protection of isoquinoline alkaloids, and has physiological significance in the clinical challenge to use isoquinoline alkaloids or their potential analogs in the treatment of CVD.

We study variants of the local models constructed by the second author and Zhu and consider corresponding integral models of Shimura varieties of abelian type. We determine all cases of good, resp. of semi-stable, reduction under tame ramification hypotheses.

Multifunctional polymer composites with high thermal conductivity are beneficial as thermal management materials for advanced electronics and technologies because of their design flexibility. Howev...

Cocenters of Hecke algebras H \mathcal {H} play an important role in studying mod ℓ \ell or C \mathbb C harmonic analysis on connected p p -adic reductive groups. On the other hand, the depth r r Hecke algebra H r + \mathcal {H}_{r^+} is well suited to study depth r r smooth representations. In this paper, we study depth r r rigid cocenters H ¯ r + r i g \overline {\mathcal {H}}^\mathrm {rig}_{r^+} of a connected reductive p p -adic group over rings of characteristic zero or ℓ ≠ p \ell \neq p . More precisely, under some mild hypotheses, we establish a Jordan decomposition of the depth r r rigid cocenter, hence find an explicit basis of H ¯ r + r i g \overline {\mathcal {H}}^\mathrm {rig}_{r^+} .

The motivation for this paper is the study of arithmetic properties of Shimura varieties, in particular the Newton stratification of the special fiber of a suitable integral model at a prime with parahoric level structure. This is closely related to the structure of Rapoport–Zink spaces and of affine Deligne–Lusztig varieties. We prove a Hodge–Newton decomposition for affine Deligne–Lusztig varieties and for the special fibers of Rapoport–Zink spaces, relating these spaces to analogous ones defined in terms of Levi subgroups, under a certain condition (Hodge–Newton decomposability) which can be phrased in combinatorial terms. Second, we study the Shimura varieties in which every non-basic $$\sigma $$ -isogeny class is Hodge–Newton decomposable. We show that (assuming the axioms of He and Rapoport in Manuscr. Math. 152(3–4):317–343, 2017) this condition is equivalent to nice conditions on either the basic locus or on all the non-basic Newton strata of the Shimura varieties. We also give a complete classification of Shimura varieties satisfying these conditions. While previous results along these lines often have restrictions to hyperspecial (or at least maximal parahoric) level structure, and/or quasi-split underlying group, we handle the cases of arbitrary parahoric level structure and of possibly non-quasi-split underlying groups. This results in a large number of new cases of Shimura varieties where a simple description of the basic locus can be expected. As a striking consequence of the results, we obtain that this property is independent of the parahoric subgroup chosen as level structure. We expect that our conditions are closely related to the question whether the weakly admissible and admissible loci coincide.

In this paper, we study some relation between the cocenter H ¯ ( G ) of the Hecke algebra H ( G ) of a connected reductive group G over a nonarchimedean local field and the cocenter H ¯ ( M ) of its Levi subgroups M. Given any Newton component of H ¯ ( G ) , we construct the induction map i ¯ from the corresponding Newton component of H ¯ ( M ) to it. We show that this map is an isomorphism. This leads to the Bernstein–Lusztig type presentation of the cocenter H ¯ ( G ) , which generalizes the work [11] on the affine Hecke algebras. We also show that the map i ¯ we constructed is adjoint to the Jacquet functor.

The affine Deligne–Lusztig variety $X_w(b)$ in the affine flag variety of a reductive group ${\mathbf G}$ depends on two parameters: the $\sigma $ -conjugacy class $[b]$ and the element w in the Iwahori–Weyl group $\tilde {W}$ of ${\mathbf G}$ . In this paper, for any given $\sigma $ -conjugacy class $[b]$ , we determine the nonemptiness pattern and the dimension formula of $X_w(b)$ for most $w \in \tilde {W}$ .

Electrospinning is sometimes used to prepare filler/polymer composite materials for thermal management owing to the linear filler orientation and convenient processing. However, the filler–polymer thermal resistance inside the electrospun fibers and the lack of effective connection between the electrospun fibers affect the filler utilization efficiency of electrospun films. In the present work, an electrospinning–electrospraying technique was applied as a new strategy to prepare filler–polymer composites, where electrospinning was used to provide the main heat conduction path, and electrospraying was adopted to connect the electrospun fibers and construct an extra heat conduction path. Finally, an electrospun–electrosprayed composite film with a thermal conductivity of 24.98 W/(m·K) at 40 wt% boron nitride nanosheet (BNNS) content was produced. The thermal conductivity of the electrospun–electrosprayed film with 30 wt% BNNS was 1.7 times that of the electrospun film. This study represents the first use of the electrospinning–electrospraying method to prepare high-thermal-conductivity composite materials, and this method shows great potential for the preparation of such materials for thermal management.

In this paper, we study the μ-ordinary locus of a Shimura variety with parahoric level structure. Under the axioms in [12] , we show that μ-ordinary locus is a union of certain maximal Ekedahl–Kottwitz–Oort–Rapoport strata introduced in [12] and we give criteria on the density of the μ-ordinary locus.

In this paper, we study the relation between the cocenter H ~ ¯ \overline {{\tilde {\mathcal H}}} and the representations of an affine pro- p p Hecke algebra H ~ = H ~ ( 0 , − ) {\tilde {\mathcal H}}={\tilde {\mathcal H}}(0, -) . As a consequence, we obtain a new criterion on supersingular representations: a (virtual) representation of H ~ {\tilde {\mathcal H}} is supersingular if and only if its character vanishes on the non-supersingular part of the cocenter H ~ ¯ \overline {\tilde {\mathcal H}} .

In this paper, we develop the theory of flag manifold over a semifield for any Kac-Moody root datum. We show that the flag manifold over a semifield admits a natural action of the monoid over that semifield associated with the Kac-Moody datum and admits a cellular decomposition. This extends the previous work of Lusztig, Postnikov, Rietsch and others on the totally nonnegative flag manifolds (of finite type) and the work of Lusztig, Speyer, Williams on the tropical flag manifolds (of finite type). As a by-product, we prove a conjecture of Lusztig on the duality of totally nonnegative flag manifold of finite type., Comment: 30 pages

The Newton strata of a reductive p-adic group are introduced in He (Forum Math Pi 6:e2, 2018) and play some role in the representation theory of p-adic groups. In this paper, we give a geometric interpretation of the Newton strata.

The study of affine Deligne-Lusztig varieties originally arose from arithmetic geometry, but many problems on affine Deligne-Lusztig varieties are purely Lie-theoretic in nature. This survey deals with recent progress on several important problems on affine Deligne-Lusztig varieties. The emphasis is on the Lie-theoretic aspect, while some connections and applications to arithmetic geometry will also be mentioned.

Let $G$ be a reductive group over an algebraically closed field and let $W$ be its Weyl group. In a series of papers, Lusztig introduced a map from the set $[W]$ of conjugacy classes of $W$ to the set $[G_u]$ of unipotent classes of $G$. This map, when restricted to the set of elliptic conjugacy classes $[W_e]$ of $W$, is injective. In this paper, we show that Lusztig's map $[W_e] \to [G_u]$ is order-reversing, with respect to the natural partial order on $[W_e]$ arising from combinatorics and the natural partial order on $[G_u]$ arising from geometry., Comment: 25 pages

Objective To identify the gaps in understanding the experience of older Chinese people receiving palliative care in nursing homes. Design A nine-step scoping review methodology was used to search for relevant literature. Methods Sixteen databases were searched for relevant studies published in English from January 1990 to August 2019. The grey literature was searched for relevant theses pertaining to the topic. Results A total of 18 studies from the United States (n = 2), mainland China (n = 1), Hong Kong (n = 13), Taiwan (n = 2) and one thesis from Hong Kong were included in the final analysis. The findings were categorised into four themes: (1) advance care planning preferences; (2) decision-making process related to palliative care; (3) palliative care experiences and barriers; and (4) practice to improve palliative care. Conclusions Given the distinctive experiences of older Chinese residents in nursing homes when faced with death and dying, cultural beliefs strongly influenced their attitudes and behaviours in receiving end-of-life care. As Chinese immigrants have become a major ethnic group in western countries, there is benefit in recognising that older Chinese people living in nursing homes and needing palliative care will face specific challenges. Culturally appropriate interventions to address older Chinese people's existential stress, grief related to loss, communication and dietary requirements, and other barriers should be developed and implemented.

In the paper four stratifications in the reduction modulo p of a general Shimura variety are studied: the Newton stratification, the Kottwitz–Rapoport stratification, the Ekedahl–Oort stratification and the Ekedahl–Kottwitz–Oort–Rapoport stratification. We formulate a system of axioms and show that these imply non-emptiness statements and closure relation statements concerning these various stratifications. These axioms are satisfied in the Siegel case.

We investigate qualitative properties of the underlying scheme of Rapoport–Zink formal moduli spaces of p-divisible groups (resp., shtukas). We single out those cases where the dimension of this underlying scheme is zero (resp., those where the dimension is the maximal possible). The model case for the first alternative is the Lubin–Tate moduli space, and the model case for the second alternative is the Drinfeld moduli space. We exhibit a complete list in both cases.

Saponins have significant bioactivities in treating cardiovascular disease. Whereas there is a lack of in-depth knowledge about how saponins prevent cardiovascular disease. Tissue factor (TF) is the major initiator of the coagulation cascade and plays an important role in hemostasis and thrombosis. However structure–activity relationships (SARs) of saponins inhibiting TF activity have not been discussed in detail at present. To further clarify the relationships between saponins and TF, in this study, 10 representative saponins were selected to study the inhibitory effect on TF procoagulant activity of monocytes by an improved chromogenic substrate method, and the possible SARs were preliminarily analyzed. Furthermore, molecular docking analysis suggested that 4 representative saponins had a good affinity with TF/FVIIa. In addition, a representative saponin, ruscogenin, decreased both messenger ribonucleic acid and protein levels of TF in human monocytes partly due to its downregulation of nuclear factor kappa-light-chain-enhancer of activated B cells and c-Jun N-terminal kinase pathways. In conclusion, this study provides further explanation for the cardiovascular protection of saponins, and the analysis of SARs between inhibiting TF activity and saponins will be helpful to explore the therapeutic TF inhibitors.

In this paper, we prove a conjecture of Kottwitz and Rapoport on a union of (generalized) affine Deligne-Lusztig varieties $X(\mu, b)_J$ for any tamely ramified group $G$ and its parahoric subgroup $P_J$. We show that $X(\mu, b)_J \neq \emptyset$ if and only if the group-theoretic version of Mazur's inequality is satisfied. In the process, we obtain a generalization of Grothendieck's conjecture on the closure relation of $\s$-conjugacy classes of a twisted loop group., Comment: 19 pages

We determine a basis of the (twisted) cocenter of graded affine Hecke algebras with arbitrary parameters. In this setting, we prove that the kernel of the (twisted) trace map is the commutator subspace (the Density theorem) and that the image is the space of good forms (the trace Paley–Wiener theorem).

We provide a direct connection between Springer theory, via Green polynomials, the irreducible representations of the pin cover $\wti W$, a certain double cover of the Weyl group $W$, and an extended Dirac operator for graded Hecke algebras. Our approach leads to a new and uniform construction of the irreducible genuine $\wti W$-characters. In the process, we give a construction of the action by an outer automorphism of the Dynkin diagram on the cohomology groups of Springer theory, and we also introduce a $q$-elliptic pairing for $W$ with respect to the reflection representation $V$. These constructions are of independent interest. The $q$-elliptic pairing is a generalization of the elliptic pairing of $W$ introduced by Reeder, and it is also related to S. Kato's notion of (graded) Kostka systems for the semidirect product $A_W=\bC[W]\ltimes S(V)$., 40 pages, added references, corrections to Appendix A

In this paper, we introduce the Newton decomposition on a connected reductive $p$-adic group $G$. Based on it we give a nice decomposition of the cocenter of its Hecke algebra. Here we consider both the ordinary cocenter associated to the usual conjugation action on $G$ and the twisted cocenter arising from the theory of twisted endoscopy. We give Iwahori–Matsumoto type generators on the Newton components of the cocenter. Based on it, we prove a generalization of Howe’s conjecture on the restriction of (both ordinary and twisted) invariant distributions. Finally we give an explicit description of the structure of the rigid cocenter.

The cocenter of an affine Hecke algebra plays an important role in the study of representations of the affine Hecke algebra and the geometry of affine Deligne–Lusztig varieties (see for example, He and Nie in Compos Math 150(11):1903–1927, 2014; He in Ann Math 179:367–404, 2014; Ciubotaru and He in Cocenter and representations of affine Hecke algebras, 2014). In this paper, we give a Bernstein–Lusztig type presentation of the cocenter. We also obtain a comparison theorem between the class polynomials of the affine Hecke algebra and those of its parabolic subalgebras, which is an algebraic analog of the Hodge–Newton decomposition theorem for affine Deligne–Lusztig varieties. As a consequence, we present a new proof of the emptiness pattern of affine Deligne–Lusztig varieties (Gortz et al. in Compos Math 146(5):1339–1382, 2010; Gortz et al. in Ann Sci Ecole Norm Sup, 2012).

Let $G$ be a complex quasi-simple algebraic group and $G/P$ be a partial flag variety. The projections of Richardson varieties from the full flag variety form a stratification of $G/P$. We show that the closure partial order of projected Richardson varieties agrees with that of a subset of Schubert varieties in the affine flag variety of $G$. Furthermore, we compare the torus-equivariant cohomology and $K$-theory classes of these two stratifications by pushing or pulling these classes to the affine Grassmannian. Our work generalizes results of Knutson, Lam, and Speyer for the Grassmannian of type $A$.

In this paper, we study the relation between the cocenter and the representation theory of affine Hecke algebras. The approach is based on the interaction between the rigid cocenter, an important subspace of the cocenter, and the dual object in representation theory, the rigid quotient of the Grothendieck group of finite dimensional representations., 31 pages

Let $W$ be an extended affine Weyl group. We prove that the minimal length elements $w_{{\mathcal{O}}}$ of any conjugacy class ${\mathcal{O}}$ of $W$ satisfy some nice properties, generalizing results of Geck and Pfeiffer [On the irreducible characters of Hecke algebras, Adv. Math. 102 (1993), 79–94] on finite Weyl groups. We also study a special class of conjugacy classes, the straight conjugacy classes. These conjugacy classes are in a natural bijection with the Frobenius-twisted conjugacy classes of some $p$-adic group and satisfy additional interesting properties. Furthermore, we discuss some applications to the affine Hecke algebra $H$. We prove that $T_{w_{{\mathcal{O}}}}$, where ${\mathcal{O}}$ ranges over all the conjugacy classes of $W$, forms a basis of the cocenter $H/[H,H]$. We also introduce the class polynomials, which play a crucial role in the study of affine Deligne–Lusztig varieties He [Geometric and cohomological properties of affine Deligne–Lusztig varieties, Ann. of Math. (2) 179 (2014), 367–404].

This paper studies affine Deligne-Lusztig varieties $X_{\tw}(b)$ in the affine flag variety of a quasi-split tamely ramified group. We describe the geometric structure of $X_{\tw}(b)$ for a minimal length element $\tw$ in the conjugacy class of an extended affine Weyl group, generalizing one of the main results in \cite{HL} to the affine case. We then provide a reduction method that relates the structure of $X_{\tw}(b)$ for arbitrary elements $\tw$ in the extended affine Weyl group to those associated with minimal length elements. Based on this reduction, we establish a connection between the dimension of affine Deligne-Lusztig varieties and the degree of the class polynomial of affine Hecke algebras. As a consequence, we prove a conjecture of G\"ortz, Haines, Kottwitz and Reuman in \cite{GHKR}., Comment: 37 pages, final version

Let $ G $ be a connected, simply connected semisimple algebraic group over the complex number field, and let $ K $ be the fixed point subgroup of an involutive automorphism of $ G $ so that $ (G, K) $ is a symmetric pair. We take parabolic subgroups $ P $ of $ G $ and $ Q $ of $ K $ respectively and consider the product of partial flag varieties $ G/P $ and $ K/Q $ with diagonal $ K $-action, which we call a \emph{double flag variety for symmetric pair}. It is said to be \emph{of finite type} if there are only finitely many $ K $-orbits on it. In this paper, we give a parametrization of $ K $-orbits on $ G/P \times K/Q $ in terms of quotient spaces of unipotent groups without assuming the finiteness of orbits. If one of $ P \subset G $ or $ Q \subset K $ is a Borel subgroup, the finiteness of orbits is closely related to spherical actions. In such cases, we give a complete classification of double flag varieties of finite type, namely, we obtain classifications of $ K $-spherical flag varieties $ G/P $ and $ G $-spherical homogeneous spaces $ G/Q $., 47 pages, 3 tables; add all the details of the classification

Let G be a semisimple group over an algebraically closed field. Steinberg has associated to a Coxeter element w of minimal length r a subvariety V of G isomorphic to an affine space of dimension r which meets the regular unipotent class Y in exactly one point. In this paper this is generalized to the case where w is replaced by any elliptic element in the Weyl group of minimal length d in its conjugacy class, V is replaced by a subvariety V' of G isomorphic to an affine space of dimension d and Y is replaced by a unipotent class Y' of codimension d in such a way that the intersection of V' and Y' is finite.

In this paper, we consider the diagonal action of a connected semisimple group of adjoint type on its wonderful compactification. We show that the semistable locus is a union of the G G -stable pieces and we calculate the geometric quotient.

Let $(W, I)$ be a finite Coxeter group. In the case where $W$ is a Weyl group, Berenstein and Kazhdan in \cite{BK} constructed a monoid structure on the set of all subsets of $I$ using unipotent $\chi$-linear bicrystals. In this paper, we will generalize this result to all types of finite Coxeter groups (including non-crystallographic types). Our approach is more elementary, based on some combinatorics of Coxeter groups. Moreover, we will calculate this monoid structure explicitly for each type., Comment: 12 pages, to appear in J. Algebra

Let $X$ be an equivariant embedding of a connected reductive group $G$ over an algebraically closed field $k$ of positive characteristic. Let $B$ denote a Borel subgroup of $G$. A $G$-Schubert variety in $X$ is a subvariety of the form $\diag(G) \cdot V$, where $V$ is a $B \times B$-orbit closure in $X$. In the case where $X$ is the wonderful compactification of a group of adjoint type, the $G$-Schubert varieties are the closures of Lusztig's $G$-stable pieces. We prove that $X$ admits a Frobenius splitting which is compatible with all $G$-Schubert varieties. Moreover, when $X$ is smooth, projective and toroidal, then any $G$-Schubert variety in $X$ admits a stable Frobenius splitting along an ample divisors. Although this indicates that $G$-Schubert varieties have nice singularities we present an example of a non-normal $G$-Schubert variety in the wonderful compactification of a group of type $G_2$. Finally we also extend the Frobenius splitting results to the more general class of $\mathcal R$-Schubert varieties., Final version, 44 pages

We prove that the Deligne–Lusztig variety associated to minimal length elements in any δ -conjugacy class of the Weyl group is affine, which was conjectured by Orlik and Rapoport in [S. Orlik, M. Rapoport, Deligne–Lusztig varieties and period domains over finite fields, arXiv: 0705.1646 ].

We study a class of perverse sheaves on some spherical varieties which include the strata of the De Concini-Procesi completion of a symmetric variety. This is a generalization of the theory of (parabolic) character sheaves., Comment: 38 pages

Let $G$ be a semisimple adjoint group over $\bold C$ and $\bar{G}$ be the De Concini-Procesi completion of $G$. In this paper, we define a Lagrangian subvariety $\Lambda$ of the cotangent bundle of $\bar{G}$ such that the singular support of any character sheaf on $\bar{G}$ is contained in $\Lambda$., Comment: 8 pages