On Discrete Hopf Fibrations, Grand Unification Groups, the Barnes-Wall, Leech Lattices, and Quasicrystals

A discrete Hopf fibration of S15 over S8 with S7 (unit octonions) as fibers leads to a 16D Polytope P16 with 4320 vertices obtained from the convex hull of the 16D Barnes-Wall lattice Λ16. It is argued (conjectured) how a subsequent 2-1 mapping (projection) of P16 onto a 8D-hyperplane might furnish the 2160 vertices of the uniform 241 polytope in 8-dimensions, and such that one can capture the chain sequence of polytopes 241,231,221,211in D=8,7,6,5dimensions, leading, respectively, to the sequence of Coxeter groups E8,E7,E6,SO(10)which are putative GUT group candidates. An embedding of the E8⊕E8and E8⊕E8⊕E8lattice into the Barnes-Wall Λ16 and Leech Λ24 lattices, respectively, is explicitly shown. From the 16D lattice E8⊕E8one can generate two separate families of Elser-Sloane 4D quasicrystals (QC’s) with H4 (icosahedral) symmetry via the “cut-and-project” method from 8D to 4D in each separate E8 lattice. Therefore, one obtains in this fashion the Cartesian product of two Elser-Sloane QC’s Q×Qspanning an 8D space. Similarly, from the 24D lattice E8⊕E8⊕E8one can generate the Cartesian product of three Elser-Sloane 4D quasicrystals (QC’s) Q×Q×Qwith H4 symmetry and spanning a 12D space.

程序语言中共归纳数据类型的一种fibrations方法

范畴论与共代数是程序语言中共归纳数据类型研究的传统方法,这些方法在语义行为分析与共归纳规则描述等方面存在一定的不足。针对以上问题,提出了一种fibrations方法以对共归纳数据类型的语义行为与共归纳规则进行研究。该方法系统分析了fibration上共归纳数据类型的重索引函子、对偶重索引函子与真值函子等基本逻辑结构,应用等式函子与商函子等工具建立共归纳数据类型与其语义行为在程序逻辑上的对应关系,深入分析共归纳数据类型的语义行为;并以基范畴上自函子及其在全范畴上保持等式的提升为工具构造共递归操作,抽象描述共归纳数据类型具有普适意义的共归纳规则;最后通过实例分析简要介绍了fibrations方法的应用。

Fibrations理论在索引归纳数据类型不确定语义中的应用

应用Fibrations理论对索引归纳数据类型的不确定语义计算进行了研究。论证了索引范畴的构造,提出了索引Fibration及其真值函子与内涵函子,建立了索引范畴上自函子的一种保持真值的提升,提出了部分F-代数的定义,并应用折叠函数等工具抽象描述了索引归纳数据类型不确定语义计算,辅以实例进行了简要分析,最后通过相关工作的论述指出了Fibrations理论研究方法的优势。

Fibrations理论在索引归纳数据类型语法构造中的应用

应用Fibrations理论对索引归纳数据类型的语法构造进行了研究。提出了索引fibration及其真值与内涵函子的定义,构造了索引与代数范畴,利用折叠函数与伴随函子等工具构造了索引范畴中一类相对复杂的索引归纳数据类型,辅以实例进行了简要分析,并通过相关工作的论述指出了Fibrations理论研究方法的优势。

基于Fibrations理论的共享系统数据模型

传统共享系统数据模型的建模方法在语义性质分析和语义行为描述方面存在不足,针对以上问题提出了一种基于Fibrations理论的共享系统数据模型。主要工作体现在两个方面:首先,应用真值函子、保持真值的提升与内涵函子并结合代数方法精确分析了语义性质,应用等式函子、保持等式的提升及商函子并结合共代数方法形式化描述了语义行为;其次,在Fibrations理论框架内构造复杂归纳与共归纳数据结构上参数化的递归与共递归操作,抽象描述具有普适意义的归纳与共归纳规则,结合实例简要介绍了Fibrations理论的应用。相对于范畴论等传统方法,简洁描述与灵活扩展的Fibrations理论对共享系统数据模型的语义性质和语义行为进行了精确分析与形式化描述,抽象描述了复杂数据结构具有普适性的归纳与共归纳规则。

Fibrations and stability for compact group actions on manifolds with local bounded Ricci covering geometry

In the study of the collapsed manifolds with bounded sectional curvature,the following two results provide basic tools:a(singular)fibration theorem by K.Fukaya[J.Differential Gcom.,1987.25(1):139156]and J.Cheeger,K.Fukaya,and M.Gromov[J.Airier.Math.Soc.,1992.5(2):327372],and the stability for isometric compact Lie group actions on manifolds by R.S.Palais[Bull.Amer.Math.Soc.,1961,67(4):362364]and K.Grove and H.Karcher[Math.Z..1973,132:1120].The main results in this paper(partially)generalize the two results to manifolds with local bounded Ricci covering geometry.

A Note on Residue Formulas for the Euler Class of Sphere Fibrations

This paper presents a definition of residue formulas for the Euler class ot eohomology-oriented sphere fibrations ε. If the base of ε is a topological manifold, a Hopf index theorem can be obtained and, for the smooth category, a generalization of a residue formula is derived for real vector bundles given in [2].

An example of special Lagrangian fibration

On the total space of the line bundle π: π*1T*P1(◎)π2*T*P1 → P1× P1, acomplete Ricci-flat Kaehler metric and a smooth special Lagrangian fibration are given.This special Lagrangian fibration is smoothly built up of 4 Harvey-Lawson's models in 4directions.

SURFACES OF GENERAL-TYPE WITH X(O_S)=1 AND FIBRATIONS OF GENUS TWO(Ⅲ)

In this series of papers, surfaces of general-type with X(O_s)=1 and fibrations of genus 2 are classified completely, and some new surfaces with invariant p_8=0 are constructed This paper will set up two kinds of numerical Campedelli surfaces with fibrations of genus 2.

On base manifolds of Lagrangian fibrations

We consider base spaces of Lagrangian fibrations from singular symplectic varieties. After defining cohomologically irreducible symplectic varieties, we construct an example of Lagrar, gian fibration whose base space is isomorphic to a quotient of the projective space. We also prove that the base space of Lagrangian fibration from a cohomologically symplectic variety is isomorphic to the projective space provided that the base space is smooth.

A NOTE ON THE RELATIVE CANONICAL IMAGE OF A NON-HYPERELLIPTIC FIBRATION OF GENUS

This paper investigates the relative 1-canonical images of non-hyperelliptic fibrations of genus 4. It is proved that if a fibre of the relative 1-canonical image ∑ is not a complete intersection in 3 , then the variety ∑ cannot be smooth on this fibre. Moreover, two examples are given to show the occurrence of such cases.

A Fibration of Categories over H_B

K. A. Hardie and K. H. Kamps investigated the track homotopy category H_B over a fixed spare B ([5]). This paper extends H_B to the track homotopy category H_b over a fixed map b: B → , such that there exists a split fibration of categories L: H_b → H_B and H_b possesses some construction as in H_B.

On M-theory on real toric fibrations

Borrowing ideas from elliptic complex geometry, we approach M-theory compactifications on real fibrations. Precisely, we explore real toric equations rather than complex ones exploited in F-theory and related dual models. These geometries have been built by moving real toric manifolds over real bases. Using topological changing behaviors, we unveil certain data associated with gauge sectors relying on affine lie symmetries.

Semipositivity of generic ordinary fibration over a curve

Let f : X → B be a generic ordinary proper fibration over a complete curve in positive characteristics, we prove that the dual of higher direct image sheaf R^1 f_*O_X is nef. As a corollary, we show that f_*ω_(S/B) is nef, if f : S → B is a fibration from a surface to a curve with generic ordinary fibres.

The Relative Canonical Algebra for Genus 4 Fibrations

In this paper,we prove that for the genus 4 fibration,the relative canonical algebra is generated in degrees ≤3.

Influence of Statins and Fibrates Drugs on Bone Health and Regeneration

In the medical and dental field, the importance and need for the study of materials and drugs for use as bone grafts or regeneration in injured areas due to the presence of fractures, infections or tumors that cause extensive loss of bone tissue is observed. Bone is a specialized, vascularized and dynamic connective tissue that changes throughout the life of the organism. When injured, it has a unique ability to regenerate and repair without the presence of scars, but in some situations, due to the size of the defect, the bone tissue does not regenerate completely. Thus, due to its importance, there is a great development in therapeutic approaches for the treatment of bone defects through studies that include autografts, allografts and artificial materials used alone or in association with bone grafts. Pharmaceuticals composed of biomaterials and osteogenic active substances have been extensively studied because they provide potential for tissue regeneration and new strategies for the treatment of bone defects. Statins work as specific inhibitors of 3-hydroxy-3-methyl-glutaryl coenzyme A reductase (HMG-CoAreductase). They represent efficient drugs in lowering cholesterol, as they reduce platelet aggregation and thrombus deposition;in addition, they promote angiogenesis, reduce the β-amyloid peptide related to Alzheimer’s disease and suppress the activation of T lymphocytes. Furthermore, these substances have been used in the treatment of hypercholesterolemia and coronary artery disease. By inhibiting HMG-CoAreductase, statins not only inhibit cholesterol synthesis, but also exhibit several other beneficial pleiotropic effects. Therefore, there has been increasing interest in researching the effects of statins, including Simvastatin, on bone and osteometabolic diseases. However, statins in high doses cause inflammation in bone defects and inhibit osteoblastic differentiation, negatively contributing to bone repair. Thus, different types of studies with different concentrations of statins have been studied to positively or negatively correlate this drug with bone regeneration. In this review we will address the positive, negative or neutral effects of statins in relation to bone defects providing a comprehensive understanding of their application. Finally, we will discuss a variety of statin-based drugs and the ideal dose through a theoretical basis with preclinical, clinical and laboratory work in order to promote the repair of bone defects.

Quantum Fibrations:Quantum Computation on an Arbitrary Topological Space

Using operator algebras,we extend the theory of quantum computation on a graph to a theory of computation on an arbitrary topological space.Quantum computation is usually implemented on finite discrete sets,and the purpose of this study is to extend this to theories on arbitrary sets.The conventional theory of quantum computers can be viewed as a simplified algebraic geometry theory in which the action of SU(2)is defined on each point of a discrete set.In this study,we extend this in general as a theory of quantum fibrations in which the action of the von Neumann algebra is defined on an arbitrary topological space.The quantum channel is then naturally extended as a net of von Neumann algebras.This allows for a more mathematically rigorous discussion of general theories,including physics and chemistry,which are defined on sets that are not necessarily discrete,from the perspective of quantum computer science.

类型系统的λω×_≤等式理论及其语义的合理性

类型系统在研究程序设计语言的理论基础方面起着十分重要的作用,特别地,带子类型的多态类型系统可刻画面向对象程序设计语言核心概念,如子类型、多态性等.为研究面向对象程序设计语言的形式理论基础,探讨了一个命名为类型系统λω×≤的带高阶子类型的多态类型系统,并利用插入子和fibration理论,引入λω×≤fibration作为该类型系统的语义模型.进一步,讨论了类型系统λω×≤的等式理论,特别是与受限全称量词有关的等式,并利用插入子的性质,证明了对于该等式理论,λω×≤fibration是合理的语义模型.

Pharmacological effects of lipid-lowering drugs on circulating adipokines

The cardioprotective effects of lipid-lowering drugs have been primarily attributed to their effects on blood lipid metabolism.However,emerging evidence indicates that lipid-lowering drugs also modulate the synthesis and secretion of adipose tissue-secreted proteins referred to as adipokines.Adipokines influence energy homeostasis and metabolism and have also been shown to modulate the vascular inflammatory cascade.The purpose of this review will be to examine the reported effects of commonly used lipid-lowering drugs(statins,fibrates,niacin and omega-3-fatty acids) on the circulating concentrations of leptin,adiponectin,tumor necrosisfactor-α(TNF-α),Retinol binding protein 4(RBP4) and resistin.Overall,the lipid-lowering drugs reviewed have minimal effects on leptin and resistin concentrations.Conversely,circulating adiponectin concentrations are consistently increased by each lipid-lowering drug reviewed with the greatest effects produced by niacin.Studies that have examined the effects of statins,niacin and omega-3-fatty acids on TNF-α demonstrate that these agents have little effect on circulating TNF-α concentrations.Niacin and fibrates appear to lower RBP4 but not resistin concentrations.The results of the available studies suggest that a strong relationship exists between pharmacological reductions in blood lipids and adiponectin that is not obvious for other adipokines reviewed.

Role of lipid-lowering agents in the management of diabetic retinopathy

Diabetic retinopathy affects a substantial proportion of patients with diabetes mellitus(DM) and is the leading cause of blindness in working-aged adults. Even though the incidence of diabetic retinopathy has declined in the last decades, its prevalence increased and is expected to rise further as a result of the increasing incidence of type 2 DM(T2DM) and the longer life expectancy of patients with DM. The pathogenesis of diabetic retinopathy is multifactorial. Some observational studies suggested an association between dyslipidemia and the development and progression of retinopathy in patients with DM but others did not confirm this association. Regarding lipid-lowering agents, studies that evaluated the role of statins in the management of these patients are mostly small and yielded discrepant results. Large randomized studies with statins in patients with T2DM showed no benefit of these agents on diabetic retinopathy but were not designed to address this effect. In contrast, both preclinical data and two large randomized controlled studies, the FIELD and the ACCORD trial, showed that fenofibrate delays the progression of diabetic retinopathy. Even though the mechanisms underpinning this favorable effect are not entirely clear, these findings suggest that fenofibrate might represent a useful tool for the management of diabetic retinopathy.