Exploring the compatibility theory of traditional Chinese medicine formulae:the disassembled prescriptions study

Traditional Chinese medicine(TCM)has become very popular in the treatment of complex diseases worldwide in recent decades.Despite the promising performance of TCM,how herbs work synergistically in a formula and their therapeutic targets remain ambiguous.This largely limits the correct use and modernization of TCM formulas clinically.The study of disassembled prescriptions is important for investigating the compatibility theory of Chinese medicines.By dissecting the mechanisms of TCM formulae,the compatibility principles of some well-known formulae,such as Realgar-Indigo naturalis,have been elucidated to a certain extent.In this review,several common methods of disassembled prescription studies are summarized,including those of single herb or mineral,sub-prescription,active ingredients or effective parts,large formulae,and systems pharmacology studies,as well as the methods of grouping based on the properties or efficacy of Chinese medicines,in order to provide evidence for formulae study.Moreover,some challenges to be addressed in disassembled prescriptions studies have been identified in this review.

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.

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.

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.

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.

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.

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.

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.

CANONICAL REPRESENTATIONS AND DEGREE OF FREEDOM FORMULAE OF ORTHOGONAL TENSORS IN N-DIMENSIONAL EUCLIDEAN SPACE

In this paper, with the help of the eigenvalue properties of orthogonal tensors in n-dimensional Euclidean space and the representations of the orthogonal tensors in 2-dimensional space, the canonical representations of orthogonal tensors in n-dimensional Euclidean space are easily gotten. The paper also gives all the constraint relationships among the principal invariants of arbitrarily given orthogonal tensor by use of Cayley-Hamilton theorem; these results make it possible to solve all the eigenvalues of any orthogonal tensor based on a quite reduced equation of m-th order, where m is the integer part ofn \2. Finally, the formulae of the degree of freedom of orthogonal tensors are given.

THE PROBABILISTIC REPRESENTATION FORMULAE FOR COSINE OPERATOR FUNCTIONS

In this paper we obtained general representation formulae for strongly continuous cosine operator functions via probabilistic approach,which include Webb's[1]and Shaw's[2]formulae and some new one as special cases.We also give the quantitative estimations for the general formulae.

BEURLING-DENY FORMULAE ON BANACH SPACES

Let B be a separable real Banach space and m be a positive measure on B. In this paper, we will establish the Beurling-Deny formulae of the Dirichlet forms on L~2(B, dm).

ON THE ERROR OF QUADRATURE FORMULAE FOR CAUCHY PRINCIPAL VALUE INTEGRALS BASED ON PIECEWISE INTERPOLATION

We consider the computation of the. Cauchy principal value mtegral by quadrature formulaeof compound type, which are obtained by replacing f by a piecewise defined function F,[;]. The behaviour of the constants m the estimates where quadrature error) is determined for fixed i and which means that not only the. order, but also the coefficient of the main term of is determined. The behaviour of these error constants is compared -with the corresponding ones obtained for the. method of subtraction of the singularity. As it turns out, these error constants have, in general, the same asymptotic behaviour.

On Female Consumption Formulae

This is an observation by the daily deliberation of China major consuming force-female,which should be a great master piece.Because of the not-in-depth study and analysis,I can only put it in the air as a clue for further research by experts.

Reliability Verification and Practical Effectiveness Evaluation of the Nursing Administration Analysis Formulae Based on PSYCHOMS^(■)

In psychiatric hospitals, the ratios between patients versus physician and patients versus nurse are low as compared to those in general hospitals. Furthermore, usages of electronic medical records are also low so that nurse administrators are limited in their ability to compile, analyze, and generate patient care staffing information for their administrative use. Psychiatric nurse administrators anticipate the development of a nursing administration analysis system that could perform personnel data simulation, manage information on nursing staff, and manage ward/ practice operations. Responding to this situation, the authors developed a nursing administration analysis system utilizing formulae from the Psychiatric Outcome Management System, PSYCHOMS&reg;to aid nurse administrators. Such formulae are awaiting patent approval. The purpose of this study was to examine the validity of the formulae and the Structured Query Language (SQL) statement, and its practical effectiveness of analyzing data. The study findings showed that two kinds of computation expressions—a classification and extraction were able to display required information desired by nurse administrators. Moreover, significant information critical to assigning staff was validated to ensure high quality of nursing care according to the function and characteristic of the hospital ward.

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.

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.

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.

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.

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.