Computing Streamfunction and Velocity Potential in a Limited Domain of Arbitrary Shape.Part I:Theory and Integral Formulae

The non-uniqueness of solution and compatibility between the coupled boundary conditions in computing velocity potential and streamfunction from horizontal velocity in a limited domain of arbitrary shape are revisited theoretically with rigorous mathematic treatments.Classic integral formulas and their variants are used to formulate solutions for the coupled problems.In the absence of data holes,the total solution is the sum of two integral solutions.One is the internally induced solution produced purely and uniquely by the domain internal divergence and vorticity,and its two components（velocity potential and streamfunction） can be constructed by applying Green＇s function for Poisson equation in unbounded domain to the divergence and vorticity inside the domain.The other is the externally induced solution produced purely but non-uniquely by the domain external divergence and vorticity,and the non-uniqueness is caused by the harmonic nature of the solution and the unknown divergence and vorticity distributions outside the domain.By setting either the velocity potential（or streamfunction） component to zero,the other component of the externally induced solution can be expressed by the imaginary（or real） part of the Cauchy integral constructed using the coupled boundary conditions and solvability conditions that exclude the internally induced solution.The streamfunction（or velocity potential） for the externally induced solution can also be expressed by the boundary integral of a double-layer（or singlelayer） density function.In the presence of data holes,the total solution includes a data-hole-induced solution in addition to the above internally and externally induced solutions.

GRADIENT ESTIMATES AND ENTROPY FORMULAE FOR WEIGHTED p-HEAT EQUATIONS ON SMOOTH METRIC MEASURE SPACES

Let （M,g, e^-fdv） be a smooth metric measure space. In this paper, we con- sider two nonlinear weighted p-heat equations. Firstly, we derive a Li-Yau type gradient estimates for the positive solutions to the following nonlinear weighted p-heat equationand f is a smooth function on M under the assumptionthat the m-dimensional nonnegative Bakry-Emery Ricci curvature. Secondly, we show an entropy monotonicity formula with nonnegative m-dimensional Bakry-Emery Ricci curva- ture which is a generalization to the results of Kotschwar and Ni [9], Li [7].

Empirical formulae for electric double-layer repulsion between two arbitrarily inclined clay particles

To understand the mesoscopic mechanism of clayey soil in view of macroscopic behavior, it is essential to quantitatively calculate the electric double-layer repulsion between arbitrarily inclined clay particles.However, suitable calculation methods with high efficiency and accuracy are still rare at present in literature. Based on a great number of numerical calculations of the repulsion between two inclined platy clay particles, explicit empirical formulae for estimating electric double-layer repulsion between clay particles are put forward. Comparison between the empirical solutions and corresponding numerical results shows that the proposed formulae have a reasonable accuracy, and application of the presented formula is easy and efficient.

Discussion on Wave Transmission Coefficient Formulae of Submerged Breakwaters

Fifteen formulae of wave transmission coefficient for submerged breakwaters obtained during last 3 decades are presented, compared, and analyzed in this paper. The dimensionless parameters mainly involved in this discussion are the relative submerged depth Re/h, relative wave height Rc/Hi, relative rubble size B/D50, relative breakwater width B√ HiL0 and wave breaker index ξ. It indicates that there exist notable differences among the computed results, which mainly originate from the limited experimental conditions and different analytical methods, even though the major tendency keeps similar. It is necessary to conduct more systematic studies to obtain better understanding about the mechanism of wave transmission over submerged breakwaters.

Evaluation of standard liver volume formulae for Chinese adults

AIM:To evaluate different standard liver volume (SLV) formula and verify the applicability of the formulae for Chinese adults.METHODS: Data from 70 cases of living donor liver transplantation (LDLT) performed at our transplantation centers between January 2008 and April 2009 were analyzed. SLV was estimated using our recently reported formula [the Chengdu formula: SLV (mL)=11.5×body weight (kg) + 334] and other reported formulae used for Chinese adults. Actual intraoperative liver volumes were obtained from a review of the patients' medical records.RESULTS: The actual right liver volume was not significantly different from the estimated right liver volume determined by the Chengdu formula, but was significantly smaller than estimates using the Heinemann, Urata, Vauthey, and Lee formulae (P<0.01), and signif icantly larger than estimates using the Fan formula (P<0.05).CONCLUSION: The Chengdu formula was demonstrated to be reliable by its application in LDLT.

Recursion-transform method and potential formulae of the m×n cobweb and fan networks

In this paper, we made a new breakthrough, which proposes a new recursion–transform（RT） method with potential parameters to evaluate the nodal potential in arbitrary resistor networks. For the first time, we found the exact potential formulae of arbitrary m × n cobweb and fan networks by the RT method, and the potential formulae of infinite and semi-infinite networks are derived. As applications, a series of interesting corollaries of potential formulae are given by using the general formula, the equivalent resistance formula is deduced by using the potential formula, and we find a new trigonometric identity by comparing two equivalence results with different forms.

ON QUADRATURE FORMULAE FOR SINGULAR INTEGRALS OF ARBITRARY ORDER

Some quadrature formulae for the numerical evaluation of singular integrals of arbitrary order are established and both the estimate of remainder and the convergence of each quadrature formula derived here are also given.

General Formulae for Two Pseudo-differential Operator

Some general formulas in the Sato theory related to the nonisospectral KP and mKP hierarchies are derived for simplifying calculations.

Gauss-Radau and Gauss-Lobatto formulae for the Jacobi weight and Gori-Micchelli weight functions

The main purpose of this work is to find for any non-negative measure, the relations between the Gauss-Radau and Gauss-Lobatto formula and Gauss formulae for the same measure. As applications, the author obtained the explicit Gauss-Radau and Gauss-Lobatto formulae for the Jacobi weight and the Gori-Micchelli weight.

The exciting and magical journey of components from compound formulae to where they fight

With its long-term empirical clinical practice and increasing number of health benefits reported,Chinese Materia Medica(CMM)is gaining increasing global acceptance.Importantly,the identification of chemical constituents in vitro and exposed forms in vivo is a prerequisite for understanding how CMM formulae prevent and treat diseases.This review systematically summarizes the exciting and magical journey of CMM components from compound formulae to where they fight,the possible structural transformation of CMM components in vitro and in vivo,and their pharmacological contribution.When a decoction is prepared,significant chemical reactions are observed,including degradation and production of polymers and self-assembling supramolecules,leading to the construction of a component library with diverse decoction structures.After ingestion,compounds pass through the intestinal and blood-brain barriers and undergo a more wonderful journey involving the gut microbiota,microbial enzymes,and endogenous drug-metabolizing enzymes(mainly liver enzymes).At this stage,they are modified and assembled into novel and complex compounds,such as newly generated metabolites,conjugates,and self-assembling superamolecules.This review might provide a strategic orientation to explore the active compounds of CMM formulae in vivo.

Chinese herbal formulae defend against Mycoplasma gallisepticum infection

Mycoplasma gallisepticum HS strain(MG-HS)is a pathogen that causes chronic respiratory disease(CRD)in chicken,which is characterized by host respiratory inflammatory damage,brings huge economic losses to the poultry industry.Recently,emerging Chinese herbal medicines(CHM)have been used to treat CRD.This study was aimed to investigate the preventive and therapeutic effects and their potential mechanisms of Chinese herbal medicinal formulae(CHMF),which consisted of 10 kinds of Chinese herbal medicine including Scutellaria,Houttuynia cordate and licorice,on MGinduced CRD in chickens.With respect to the preventive effect,the results showed that CHMF could effectively recover the MG-induced decrease on body weight and feed conversion ratio.Histopathological analysis showed that both prevention and treatment of CHMF could significantly alleviate the severe respiratory inflammation induced by MG infection.Moreover,compared with the MG infection group,both the prevention groups and the treatment groups of CHMF could effectively reduce the expression of MG adhesion protein(p MGA1.2)to inhibit the proliferation of MG,and thus effectively inhibit the expression of MG-induced inflammatory factors interleukin-1β(IL-1β)and tumour necrosis factor-α(TNF-α).In summary,these findings confirm that CHMF can protect chickens from various tissue damage caused by MG infection and has no adverse effects on the performance of chickens in the short term.And its efficacy against MG is equal to or better than that of tiamulin.

Pharmacologic mechanisms mining and prediction of Xiaoer Qixing Cha Formulae in the treatment of infantile functional dyspepsia based on chemical analysis by UPLC-QTOF/MS and interactive network pharmacology

Objective: To explore the main chemical compounds in Xiaoer Qixing Cha Formulae (XQCF), and investigate its mechanisms for the treatment of infantile functional dyspepsia (IFD). Methods: The chemical components were identified by UPLC-QTOF/MS analytic technique. Targets of the compounds were screened from TCMSP and SWISS database, and disease targets were screened from OMIM and TTD online database. Candidate targets of compounds were mapped to the disease targets as predict therapeutic targets for XQCF. Several networks were constructed and analyzed by Cytoscape ver. 3.2.1. Meanwhile, prescription compatibility in XQCF was interpreted from the network perspective based on distribution of the number of targets. Furthermore, Gene Ontology (GO) enrichment analysis and KEGG pathway analysis were operated via Clue Go to illustrate complex relationships between the potential targets and pharmacological mechanisms. Results: A total of fifty-three compounds were recognized or tentatively characterized belonging to XQCF based on MS data and online chemical database. Sixty-three therapeutic targets were screened. AKT1, FOS, SLC6A4, COMT and 5-HT receptors were focused as therapeutic targets of XQCF. Pathways including carbohydrate digestion and absorption, serotonergic synapse, calcium signaling pathway and cAMP signaling pathway were predicted as significant regulatory pathways. The results indicated that the predicted targets and pathways related in brain-gut axis to a great extent, which could be potential pharmacological mechanism of XQCF for the treatment of IFD. Conclusions: The findings in this study provided the experimental and theoretical basis for further research for XQCF. Those also illustrated a reasonable method worth intensive study on pharmacodynamic mechanisms of TCM Formulae.

Analysis of new therapeutic strategies for diabetes mellitus based on traditional Chinese medicine'xiaoke'formulae

Objective:To develop new therapeutic strategies for diabetes mellitus(DM)by analyzing the mechanisms of action of traditional Chinese medicine(TCM)'xiaoke'formulae(TCM prescriptions for remedying xiaoke).Methods:We characterized 291 xiaoke formulae,including the herbs contained,chemical composition,constituents'targets,and corresponding genes.Xiaoke-related genes were retrieved based on the relationships of constituents'targets and xiaoke formulae,and a threshold of over 95.88%occurrence of each constituent target in the 291 TCM formulae served as a definition for xiaoke-related genes.Upon comparison with DM-related genes in the DisGeNET database,the genes differing in expression between cases administered TCM and synthetic drugs were explored using a TCM grammar system.Results:The results showed that xiaoke formulae and 14 exclusively xiaoke-related genes were significantly associated with multiple biological processes closely related to DM and diabetic complications(P<.01).Moreover,intervention in the expression of these xiaoke-related genes would affect DM-related genes directly or indirectly.Conclusion:The 14 xiaoke-related genes APEX1,EHMT2,TSHR,CBX1,FEN1,GMNN,JUN,KMT2A,MAPT,POLl,USP1,PIN1,POLB,and POLK can serve as candidate genes for antidiabetic drug design.Compared with DM-related genes in DisGeNET,intervention in the expression of 14 xiaoke-related genes by TCM formulae has the potential to not only lower blood glucose,but also reduce the occurrence of some side effects and inhibit the development of diabetic complications.These findings will contribute to the discovery of new strategies for treating DM.

Research on Herb Pairs of Classical Formulae of ZHANG ZhongJing Using Big Data Technology

Objective To analyze various herbal combinations in Treatise on Exogenous Febrile Diseases(Shang Han Lun,《伤寒论》)and Synopsis of Prescriptions of the Golden Chamber(Jin Gui Yao Lve,《金匮要略》),seeking to identify fundamental rules dictating the selection of herbal combinations through probability models and big data technology.Methods A total of 252 formulae were collected from Treatise on Exogenous Febrile Diseases(Shang Han Lun,《伤寒论》)and Synopsis of Prescriptions of the Golden Chamber(Jin Gui Yao Lve,《金匮要略》)by ZHANG Zhong-Jing.Formulae were then preprocessed with all herb names standardized.The concepts of candidate herb pair and candidate herb pair probability were proposed to analyze the rules of combinations in classical formulae based on probability statistics.MapReduce parallel computing framework of distributed big data technology was adopted to analyze large data samples combined with inverted index algorithm.Results The results showed that the core herbs were Glycyrrhizae Radix Rhizoma(Gan Cao,甘草),Cinnamomi Ramulus(Gui Zhi,桂枝),Zingiberis Rhizoma Recens(Sheng Jiang,生姜),Jujubae Fructus(Da Zao,大枣),Paeoniae Radix Alba(Bai Shao,白芍),etc.43 high-frequency pairs co-occurring 10 times or above were extracted,and 35 of these combinations were recognized as traditional herb pairs,such as Cinnamomi Ramulus(Gui Zhi,桂枝)-Glycyrrhizae Radix Rhizoma(Gan Cao,甘草),Zingiberis Rhizoma Recens(Sheng Jiang,生姜)-Jujubae Fructus(Da Zao,大枣),and Cinnamomi Ramulus(Gui Zhi,桂枝)-Ginseng Radix Et Rhizoma(Ren Shen,人参).The other 8 pairs of combinations,such as Paeoniae Radix Alba(Bai Shao,白芍)-Zingiberis Rhizoma Recens(Sheng Jiang,生姜),Paeoniae Radix Alba(Bai Shao,白芍)-Jujubae Fructus(Da Zao,大枣),and Zingiberis Rhizoma Recens(Sheng Jiang,生姜)-Ginseng Radix Et Rhizoma(Ren Shen,人参),were not defined traditionally,but in connection with commonly used herbs.Classical formulae took the core herbs as principles,focusing on tonifying deficiency,strengthening the spleen and the stomach,strengthening the healthy Qi,and eliminating pathogenic factors.The compatibility pattern of properties involved was mainly acrid and sweet,which reflected the compatibility laws of benefiting Qi and tonifying Yang,replenishing Qi and nourishing blood,etc.Conclusions The research of classical formulae provides common understanding of some basic rules that have been adopted to tackle common illnesses/diseases using herbal medicine.The results help to reinforce theoretical understanding and development of traditional Chinese medicine(TCM),and revealing the hidden rules of combination in TCM data.Analyzing wider data samples of various herbal combinations through computation and big data technology can further optimize the use of TCM.

Therapeutic Actions of the Chinese Herbal Formulae with Cold and Heat Properties and Their Effects on Ultrastructures of Synoviocytes in Rats of the Collagen-Induced Arthritis

The therapeutic actions of Qing Luo Yin (QLY清络饮) with heat property and Wen Luo Yin (WLY温络饮) with cold property on pain, swelling of the ankle, arthritis index and ultrastructures of synoviocytes were compared in rats of type II collagen-induced arthritis (CIA), with tripterygium glycosidorum (TG) used as control. The results indicated that both QLY and WLY could reduce pain, swelling of the ankle and the arthritis index of CIA, and QLY had better effects in reducing the swelling of the ankle and controlling the secondary pathological lesions as compared with WLY. Investigation on the ultrastructures of synoviocytes indicated that both QLY and WLY could reduce the number of Golgi apparatus, rough surface endoplasmic reticulum, dense bodies, matrix filaments and vacuoles so as to suppress the excessive secretion of synoviocytes in rats of CIA.

ASYMPTOTIC FORMULAE FOR BIVARIATE MELLIN CONVOLUTION OPERATORS

In this paper some Voronovskaya approximation formulae for a class of Mellin convolution operators of the type （Twf）（x,y）=∫R^2＋Kw（tx^-1,vy^-1）f（t,v）dtdv/tv are given. Moreover, various examples are discussed.

The Maximum Trigonometric Degrees of Quadrature Formulae with Prescribed Nodes

The purpose of this paper is to study the maximum trigonometric degree of the quadrature formula associated with m prescribed nodes and n unknown additional nodes in the interval（-π, π]. We show that for a fixed n, the quadrature formulae with m and m ＋ 1 prescribed nodes share the same maximum degree if m is odd. We also give necessary and sufficient conditions for all the additional nodes to be real, pairwise distinct and in the interval（-π, π] for even m, which can be obtained constructively. Some numerical examples are given by choosing the prescribed nodes to be the zeros of Chebyshev polynomials of the second kind or randomly for m ≥ 3.

General Interpolation Formulae for Barycentric Blending Interpolation

General interpolation formulae for barycentric interpolation and barycen- tric rational Hermite interpolation are established by introducing multiple parameters, which include many kinds of barycentric interpolation and barycentric rational Her- mite interpolation. We discussed the interpolation theorem, dual interpolation and special cases. Numerical example is given to show the effectiveness of the method.

Indomie Noodle Healthy Formulae Instead of the Commercial Formula

This investigation was carried out to evaluate some different seasoning made of onion, garlic, red chili, oregano, marjoram, basil, rosemary, cumin and black pepper to give light and healthy formulae to add to instant indomie noodle. Antioxidants were assessed in raw materials and their formulae, also sensory properties were evaluated in different instant indomie noodle seasoning formulae. The results in raw materials explored that the seasoning contains large amounts of antioxidants content, total carotenoids, volatile oil and antioxidant activity compared with the commercial formula. Corn oil was used as a carrier for the commercial formula and separated three tested spice formulae in ratio 1:100 w/w. Three chosen tested formulas;onion, garlic, red chili 1);oregano, marjoram, basil 2) and rosemary, cumin, black pepper 3) were used in the research. The results indicated that formula 3 has higher antioxidant activity (119.00%) than formula 1 and 2 (83.33% and 62.33%, respectively). Meanwhile, the results from sensory evaluation showed that no significant difference appeared from the different spice formulae. Biological experiment was carried out for these formulae and measured the liver reduced glutathione (GSH), superoxide dismutase (SOD), malonaldehyde (MDA), serum liver enzymes aspartate and alanine aminotransferases and alkaline phosphatase (AST, ALT and ALP), serum total protein, albumin and globulin also, renal function (uric acid, urea and creatinine) in rats fed on basal diet including oil carried the commercial formula or instant indomie noodle tested seasoning formulae. The results illustrated that the different instant indomie noodle seasoning formulae gave better results than the commercial formula in liver and renal functions. It could be recommended that consuming the suggested different seasoning formulae instead of the commercial questioned one as sodium glutamate prevent many harmful effects. It should be done occasionally, especially when the need for indomie noodles arises especially for children. This is because it contains the necessary nutrients as antioxidants and acceptable taste for healthy living in moderate proportion.

Fanlian Huazhuo Formula alleviates high-fat diet-induced nonalcoholic fatty liver disease by modulating autophagy and lipid synthesis signaling pathway

BACKGROUND Fanlian Huazhuo Formula(FLHZF)has the functions of invigorating spleen and resolving phlegm,clearing heat and purging turbidity.It has been identified to have therapeutic effects on type 2 diabetes mellitus(T2DM)in clinical application.Non-alcoholic fatty liver disease(NAFLD)is frequently diagnosed in patients with T2DM.However,the therapeutic potential of FLHZF on NAFLD and the underlying mechanisms need further investigation.AIM To elucidate the effects of FLHZF on NAFLD and explore the underlying hepatoprotective mechanisms in vivo and in vitro.METHODS HepG2 cells were treated with free fatty acid for 24 hours to induce lipid accumulation cell model.Subsequently,experiments were conducted with the different concentrations of freeze-dried powder of FLHZF for 24 hours.C57BL/6 mice were fed a high-fat diet for 8-week to establish a mouse model of NAFLD,and then treated with the different concentrations of FLHZF for 10 weeks.RESULTS FLHZF had therapeutic potential against lipid accumulation and abnormal changes in biochemical indicators in vivo and in vitro.Further experiments verified that FLHZF alleviated abnormal lipid metabolism might by reducing oxidative stress,regulating the AMPKα/SREBP-1C signaling pathway,activating autophagy,and inhibiting hepatocyte apoptosis.CONCLUSION FLHZF alleviates abnormal lipid metabolism in NAFLD models by regulating reactive oxygen species,autophagy,apoptosis,and lipid synthesis signaling pathways,indicating its potential for clinical application in NAFLD.