P-kernel Normal Systems in Weakly P-inversive Semigroups

In this paper, we first give the concept of weakly P-inversive semigroup S（P）. Then we describe the strong P-congruences on S（P） in terms of their P-kernel normal systems. It is proved that there is a bijection between the strong P-congruences and the P-kernel normal systems. Finally, it is also prove that the lattice of strong P-congruences and the lattice of P-kernel normal systems on S（P） are isomorphic.

Some Characterizations of Left Weakly Regular Ordered Semigroups

In this paper, the notion of left weakly regular ordered semigroups is introduced. Furthermore, left weakly regular ordered semigroups are characterized by the properties of their left ideals, right ideals and （generalized） bi-ideals, and also by the properties of their fuzzy left ideals, fuzzy right ideals and fuzzy （generalized） bi-ideals.

ASYMPTOTIC BEHAVIOR FOR COMMUTATIVE SEMIGROUPS OF ALMOST ASYMPTOTICALLY NONEXPANSIVE TYPE MAPPINGS

This article introduces the concept of commutative semigroups of almost asymptotically nonexpansive-type mappings in a Banach space X which has the Opial property and whose norm is UKK, and establishes the weak convergence theorems for almostorbits of this class of commutative semigroups. The author improves, extends and develops some recent and earlier results.

Weakly Noether Symmetry for Nonholonomic Systems of Chetaev's Type

In the paper [J. of Beijing Institute of Technology 26 （2006） 285] the authors provided the definition of weakly Noether symmetry. We now discuss the weakly Noether symmetry for non-holonomic system of Chetaev＇s type, and present expressions of three kinds of conserved quantities by weakly Noether symmetry. Finally, the application of this new result is shown by a practical example.

FREUD-BUTZER-HAHN TYPE QUANTITATIVE THEOREMS FOR PROBABILISTIC REPRESENTATIONS OF(C_0)OPERATOR SEMIGROUPS

In this paper,we shall exploit the Freud method in the Classical operator approximation theory to im- prove known quantitative estimalions with an emphasis on Calculah' on the generic constants.

A Class of ＊-simple Type A ω~2 -semigroups （Ⅰ）

In this paper, we study ＊-simple type A ω2 -semigroups in which D＊= D and D＊｜ES = Md by the generalized Bruck-Reilly extension and obtain its structure theorem. We also obtain a criterion for isomorphisms of two such semigroups.

Semigroup of Weakly Continuous Operators Associated to a Generalized Schrödinger Equation

In this work, we prove the existence and uniqueness of the solution of the generalized Schrödinger equation in the periodic distributional space P’. Furthermore, we prove that the solution depends continuously respect to the initial data in P’. Introducing a family of weakly continuous operators, we prove that this family is a semigroup of operators in P’. Then, with this family of operators, we get a fine version of the existence and dependency continuous theorem obtained. Finally, we provide some consequences of this study.

Group of Weakly Continuous Operators Associated to a Generalized Schrödinger Type Homogeneous Model

In this work, we prove the existence and uniqueness of the solution of the generalized Schrödinger type homogeneous model in the periodic distributional space P’. Furthermore, we prove that the solution depends continuously respect to the initial data in P’. Introducing a family of weakly continuous operators, we prove that this family is a group of operators in P’. Then, with this family of operators, we get a fine version of the existence and dependency continuous theorem obtained. Finally, we give some remarks derived from this study.

Two-weight weak-type inequalities for potential type operators

For the potential type operatorTФf（x）=∫RnФ（x-y）f（y）dy,where Ф is a non-negative locally integrable function on R^n and satisfies weak growth condition, a two-weight weak-type （p,q） inequality for TФ is obtained.

血清sTWEAK、sLOX-1与H型高血压合并HFpEF患者颈动脉粥样硬化的关系

目的研究血清可溶性肿瘤坏死因子样凋亡弱诱导因子(sTWEAK)、可溶性凝集素样氧化型低密度脂蛋白受体-1(sLOX-1)与H型高血压合并射血分数保留的心力衰竭(HFpEF)患者颈动脉粥样硬化的关系。方法选取2021年2月至2023年3月沧州中西医结合医院收治的161例H型高血压合并HFpEF患者,按是否发生颈动脉粥样硬化分为硬化组与非硬化组。同期选取80例于我院体检的健康的志愿者作为对照组。收集受试者的临床资料,采用酶联免疫吸附法检测血清sTWEAK、sLOX-1水平,比较H型高血压合并HFpEF患者与对照组血清sTWEAK、sLOX-1水平,采用多因素logistic回归分析患者发生颈动脉粥样硬化的影响因素,受试者工作特征(ROC)曲线分析血清sTWEAK、sLOX-1对患者发生颈动脉粥样硬化的预测价值。结果161例患者中65例发生颈动脉粥样硬化,发生率为40.37%(65/161),未发生颈动脉粥样硬化者96例。两组在年龄、吸烟、血脂四项等方面比较,差异有统计学意义(P<0.05)。硬化组与非硬化组血清sTWEAK水平低于对照组,sLOX-1水平高于对照组(P<0.05);且硬化组sTWEAK水平低于非硬化组,sLOX-1水平高于非硬化组(P<0.05)。多因素logistic回归分析显示,HDL-C、sTWEAK、年龄、LDL-C、sLOX-1水平是患者发生颈动脉粥样硬化的影响因素(P<0.05)。ROC曲线显示,血清sTWEAK、sLOX-1联合检测对发生颈动脉粥样硬化的预测曲线下面积(AUC)为0.842,预测效能高于两指标单独检测。结论H型高血压合并HFpEF患者的血清sTWEAK水平下降、sLOX-1水平上升,与颈动脉粥样硬化发生有关,两者联合检测对颈动脉粥样硬化的发生具有一定预测价值。

A FOUR-WEIGHT WEAK TYPE MAXIMAL INEQUALITY FOR MARTINGALES

In this article, some necessary and sufficient conditions are shown in order that weighted inequality of the form ■holds a.e. for uniformly integrable martingales f =(f_n)n≥0 with some constant C > 0,where Φ_1,Φ_2 are Young functions, w_i(i = 1,2,3, 4) are weights, f~* =sup n≥0 |f_n| and f_∞=lim n→∞ f_n a.e. As an application, two-weight weak type maximal inequalities of martingales are considered, and particularly a new equivalence condition is presented.

BOUNDEDNESS OF VARIATION OPERATORS ASSOCIATED WITH THE HEAT SEMIGROUP GENERATED BY HIGH ORDER SCHRODINGER TYPE OPERATORS

In this article,we derive the Lp-boundedness of the variation operators associated with the heat semigroup which is generated by the high order Schrodinger type operator(—Δ)^2+V%2 in R%n(n≥5)with V being a nonnegative potential satisfying the reverse Holder inequality.Furt her more,we prove the boundedness of the variation operators on associated Morrey spaces.In the proof of the main results,we always make use of the variation inequalities associated with the hea t semigroup genera ted by the biharmonic operator(-Δ)2.

WEAK TYPE INEQUALITY FOR THE MAXIMAL OPERATOR OF WALSH-KACZMARZ-MARCINKIEWICZ MEANS

The main aim of this article is to prove that the maximal operator σ^k＊ of the Marcinkiewicz-Fejer means of the two-dimensional Fourier series with respect to Walsh- Kaczmarz system is bounded from the Hardy space H2/3 to the space weak-L2/3.

WEAK TYPE INEQUALITIES FOR FRACTIONAL INTEGRAL OPERATORS ON GENERALIZED NON-HOMOGENEOUS MORREY SPACES

We obtain weak type （1, q） inequalities for fractional integral operators on generalized non-homogeneous Morrey spaces. The proofs use some properties of maximal operators. Our results are closely related to the strong type inequalities in [13, 14, 15].

TWO-WEIGHT WEAK-TYPE MAXIMAL INEQUALITIES FOR MARTINGALES

In this article, some necessary and sufficient conditions are shown in order that the inequality of the form Ф1（λ）Pu（f^＊〉λ）≤Ev （Ф2（C｜f∞｜）） holds with some constant C 〉 0 independent of martingale f = （fn）n≥0 and λ 〉 0, where Фl and Ф2 are a pair of Young functions, f^＊=sup n≥0｜fn｜ adn f∞=lim n→∞ fn a.e.

WEIGHTED WEAK TYPE ESTIMATES INVOLVING SPACES GENERATED BY BLOCKS

The problem studied in this paper is how to establish weighted estimates of weak type near L^1 for those operators that are not of weak type(1,1).

Traditional Chinese Medicine-Based Subtyping of Early-Stage Type 2 Diabetes Using Plasma Metabolomics Combined with Ultra-Weak Photon Emission

The prevalence of type 2 diabetes mellitus(T2DM)is increasing rapidly worldwide.Because of the limited success of generic interventions,the focus of the disease study has shifted toward personalized strategies,particularly in the early stages of the disease.Traditional Chinese medicine(TCM)is based on a systems view combined with personalized strategies and has improved our knowledge of personalized diagnostics.From a systems biology perspective,the understanding of personalized diagnostics can be improved to yield a biochemical basis for such strategies;for example,metabolomics can be used in combination with other system-based diagnostic methods such as ultra-weak photon emission(UPE).In this study,we investigated the feasibility of using plasma metabolomics obtained from 44 pre-T2DM subjects to stratify the following TCM-based subtypes:Qi-Yin deficiency,Qi-Yin deficiency with dampness,and Qi-Yin deficiency with stagnation.We studied the relationship between plasma metabolomics and UPE with respect to TCM-based subtyping in order to obtain biochemical information for further interpreting disease subtypes.Principal component analysis of plasma metabolites revealed differences among the TCM-based pre-T2DM subtypes.Relatively high levels of lipids(e.g.,cholesterol esters and triglycerides)were important discriminators of two of the three subtypes and may be associated with a higher risk of cardiovascular disease.Plasma metabolomics data indicate that the lipid profile is an essential component captured by UPE with respect to stratifying subtypes of T2DM.The results suggest that metabolic differences exist among different TCM-based subtypes of pre-T2DM,and profiling plasma metabolites can be used to discriminate among these subtypes.Plasma metabolomics thus provides biochemical insights into system-based UPE measurements.

Adsorption behavior of gel-type weak acid resin (110-H) for Pb^(2+)

The adsorption properties of a novel gel-type weak acid resin (110-H) for Pb2+ were investigated using chemical methods and IR spectrometry.The optimal adsorption condition of 110-H for Pb2+ is at pH=6.49 in HAc-NaAc medium and the statically saturated adsorption capacity is 485 mg/g at 298 K.Pb2+ adsorbed on 110-H resin can be eluted with 0.025 mol/L HCl quantificationally.The adsorption rate constants determined under the temperatures of 288,298,308 and 318 K are 2.46×10-5,3.82×10-5,4.46×10-5 and 5.71×10-5 s-1,respectively.The apparent activation energy,Ea,is 18.1 kJ/mol and the thermodynamic parameters of adsorption,ΔH=20.9 kJ/mol,ΔS=161 J/(mol.K) and ΔG298 K =-48.0 kJ/mol,respectively.The adsorption behavior of 110-H resin for Pb2+ accords with the Langmuir isotherm.Infrared spectra show that the oxygen atoms of the functional group of resin coordinate with Pb2+ to form the coordination bands.

LIMITING WEAK-TYPE BEHAVIORS FOR CERTAIN LITTLEWOOD-PALEY FUNCTIONS

In this paper, we establish the following limiting weak-type behaviors of Littlewood-Paley g-function g_φ: for nonnegative function f∈ L^1(R^n),■and ■where f_t(x) =t^(-n)f(t^(-1) x) for t > 0. Meanwhile, the corresponding results for Marcinkiewicz integral and its fractional version with kernels satisfying L_α~q-Dini condition are also given.

A Class of Left E-adequate Semigroups

In this paper we establish a construction of a class of left E-adequate semigroups by using semilattices of cancellative monoids and fundamental left E-adequate semigroups. We first introduce concepts of type μ^＋（μ^＊,μ ） abundant semigroups and type μ^＋left E-adequate semigroups. In fact, regular semigroups are type μ^＋abundant semigroups and inverse semigroups are type μ^＋left E-adequate semigroups. Next, we construct a special kind of algebras called E^＋-product. It is proved that every E^＋-product is a type μ^＋left E-adequate semigroup, and every type μ^＋left E-adequate semigroup is isomorphic to an E^＋-product of a semilattice of cancellative monoids with a fundamental left E-adequate semigroup. Finally, as a corollary of the main result, it is deduced that every inverse semigroup is isomorphic to an E^＋-product of a Clifford semigroup by a fundamental inverse semigroup.