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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.

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.

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.

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.

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

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

We give a definition of character sheaves on the group compactification which is equivalent to Lusztig's definition in \cite{L3}. We also prove some properties of the character sheaves on the group compactification., 22 pages. Final version

Activated protein C (APC) requires both Ca2+ and Na+ for its optimal catalytic function. In contrast to the Ca2+-binding sites, the Na+-binding site(s) of APC has not been identified. Based on a recent study with thrombin, the 221-225 loop is predicted to be a potential Na+-binding site in APC. The sequence of this loop is not conserved in trypsin. We engineered a Gla domainless form of protein C (GDPC) in which the 221-225 loop was replaced with the corresponding loop of trypsin. We found that activated GDPC (aGDPC) required Na+ (or other alkali cations) for its amidolytic activity with dissociation constant (Kd(app)) = 44.1 +/- 8.6 mM. In the presence of Ca2+, however, the requirement for Na+ by aGDPC was eliminated, and Na+ stimulated the cleavage rate 5-6-fold with Kd(app) = 2.3 +/- 0.3 mM. Both cations were required for efficient factor Va inactivation by aGDPC. In the presence of Ca2+, the catalytic function of the mutant was independent of Na+. Unlike aGDPC, the mutant did not discriminate among monovalent cations. We conclude that the 221-225 loop is a Na+-binding site in APC and that an allosteric link between the Na+ and Ca2+ binding loops modulates the structure and function of this anticoagulant enzyme.

Human protein S (PS) potentiates the anticoagulant activity of human but not bovine activated protein C (APC), whereas bovine PS is a cofactor to APC from both species. The structural requirements for the specificity of the APC cofactor function of human PS are located in its thrombin-sensitive region (TSR) and the first epidermal growth factor (EGF1)-like module. To elucidate which residues in these two modules determine the specificity of the APC cofactor activity, 41 human PS mutants were expressed. All mutants were cofactors to human APC and some also to bovine APC. Residues in TSR (positions 49 and 52) and EGF1 (residues 97 and 106) together determined the specificity of the APC cofactor function, whereas substitution of individual residues did not change specificity. Bovine PS, and mutants expressing cofactor activity to bovine APC, stimulated phospholipid binding of bovine APC. In contrast, human PS and mutants lacking cofactor activity to bovine APC failed to support binding of bovine APC to phospholipids. These data indicate that residues in TSR and EGF1 cause the specificity of the APC cofactor activity and support the concept that key residues in these two modules interact with APC on the phospholipid surface.

Expression of the endothelial cell protein C receptor (EPCR) gene in mammalian cells imparts the capacity to bind activated protein C (APC) or protein C. Immunochemical analysis of CCD41, apparently the murine homologue of EPCR, suggested centrosomal localization, raising questions about the location of the EPCR gene product and its role in protein C binding. In this study, we express a soluble form of EPCR, demonstrate EPCR expression on the cell surface, and direct binding between soluble EPCR and protein C/APC. Affinity purified polyclonal and a monoclonal antibody against EPCR bound to the cell surface of EPCR-transfected cells but not to control cells. A 49-kDa protein, a mass similar to soluble EPCR, was immunoprecipitated from the cell surface of endothelium and cells transfected with human EPCR but not from control cells. The FLAG™ antibody and APC bound to cells expressing an EPCR construct containing the FLAG™ epitope located in a putative extracellular domain, whereas an EPCR construct truncated just before the putative transmembrane domain produced only soluble EPCR antigen. Soluble EPCR inhibited APC binding to EPCR expressing cells in a concentration-dependent fashion, Kd(app) = 29 nM and bound to immobilized protein C in a Ca2+-dependent fashion. Thus, EPCR is a type 1 transmembrane protein that binds directly to APC.