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Neuropathic pain is a debilitating pathological pain condition with a great therapeutic challenge in clinical practice. Currently used analgesics produce deleterious side effects. Therefore, it is necessary to investigate alternative medicines for neuropathic pain. Chinese herbal medicines have been widely used in treating intractable pain. Compelling evidence revealed that the bioactive alkaloids of Chinese herbal medicines stand out in developing novel drugs for neuropathic pain due to multiple targets and satisfactory efficacy. In this review, we summarize the recent progress in the research of analgesic effects of 20 alkaloids components for peripheral neuropathic pain and highlight the potential underlying molecular mechanisms. We also point out the opportunities and challenges of the current studies and shed light on further in-depth pharmacological and toxicological studies of these bioactive alkaloids. In conclusion, the alkaloids hold broad prospects and have the potentials to be novel drugs for treating neuropathic pain. This review provides a theoretical basis for further applying some alkaloids in clinical trials and developing new drugs of neuropathic pain.

Male infertility has affected many families around the world. However, due to the mechanism underlying male reproductive system dysfunction are not completely elucidated, the use of drugs for male reproductive system dysfunction treatment only insignificant higher pregnancy outcomes, low-quality evidence suggests that clinical pregnancy rates may increase. Therefore, the focus in the future will be on developing more viable treatment options to prevent or treatment of male reproductive system dysfunction and achieve the purpose of improving fertility. Interestingly, natural products, as the potential inhibitors for the treatment of male reproductive system dysfunction, have shown a good therapeutic effect. Among many natural products, flavonoids have been extensively investigated for the treatment of male reproductive system dysfunction, such as testicular structural disruption, spermatogenesis disturbance and sperm quality decline. Flavonoids have been reported to have antioxidant, anti-inflammatory, immune stimulating, anti-apoptotic, anticarcinogenic, anti-allergic and antiviral activities, investigating for the treatment of male reproductive system dysfunction. In this review, we evaluate the therapeutic effects of flavonoids on male reproductive system dysfunction under different cellular scenarios and summarize the therapeutic strategies of flavonoids based on the aforementioned retrospective analysis. In the end, we describe some perspective research areas relevant to the application of flavonoids in the treatment of male reproductive system dysfunction.

International audience; We prove several conjectures made by Z.-W. Sun on the existence of permutations conditioned by certain rational functions. Furthermore, we fully characterize all integer values of the "inverse difference" rational function. Our proofs consist of both investigation of the mathematical properties of the rational functions and brute-force attack by computer for finding special permutations.

The Poupard polynomials are polynomials in one variable with integer coefficients, with some close relationship to Bernoulli and tangent numbers. They also have a combinatorial interpretation. We prove that every Poupard polynomial has all its roots on the unit circle. We also obtain the same property for another sequence of polynomials introduced by Kreweras and related to Genocchi numbers. This is obtained through a general statement about some linear operators acting on palindromic polynomials., 10 pages, 1 figure

In 1998, Allouche, Peyri\`{e}re, Wen and Wen showed that the Hankel determinant $H_n$ of the Thue-Morse sequence over $\{-1,1\}$ satisfies $H_n/2^{n-1}\equiv 1~(\mathrm{mod}~2)$ for all $n\geq 1$. Inspired by this result, Fu and Han introduced \emph{apwenian} sequences over $\{-1,1\}$, namely, $\pm 1$ sequences whose Hankel determinants satisfy $H_n/2^{n-1}\equiv 1~(\mathrm{mod}~2)$ for all $n\geq 1$, and proved with computer assistance that a few sequences are apwenian. In this paper, we obtain an easy to check criterion for apwenian sequences, which allows us to determine all apwenian sequences that are fixed points of substitutions of constant length. Let $f(z)$ be the generating functions of such apwenian sequences. We show that for all integer $b\ge 2$ with $f(1/b)\neq 0$, the real number $f(1/b)$ is transcendental and its irrationality exponent is equal to $2$. Besides, we also derive a criterion for zero-one apwenian sequences whose Hankel determinants satisfy $H_n\equiv 1~(\mathrm{mod}~2)$ for all $n\geq 1$. We find that the only zero-one apwenian sequence, among all fixed points of substitutions of constant length, is the period-doubling sequence. Various examples of apwenian sequences given by substitutions with projection are also given. Furthermore, we prove that all Sturmian sequences over $\{-1,1\}$ or $\{0,1\}$ are not apwenian. And we conjecture that fixed points of substitution of non-constant length over $\{-1,1\}$ or $\{0,1\}$ can not be apwenian., Comment: 27 pages

Background Blood-testis barrier (BTB) impairments is one of the major secondary complications of diabetes. Betaine (BET) is the important active ingredients isolated from Lycium barbarum, which exhibits numerous pharmacological activities such as antioxidant, anti-diabetic, and anti-inflammatory effects. This study aimed to establish whether BET contributes to the recovery from BTB dysfunction in streptozotocin (STZ) induced diabetic mice. Methods BET (200, 400, 800 mg/kg) was orally administered to diabetic mice for 8 weeks. Testis tissues were collected for histopathological and biochemical analysis, the reproductive organ weight was estimated. Antioxidant enzyme activity and BTB associated protein expressions were determined with their corresponding assay kits and western blot analysis. The results revealed that BET significantly improved the weight of the reproductive organs and testicular morphology in diabetic mice. Furthermore, reactive oxygen species (ROS) and malondialdehyde (MDA) levels were significantly reduced, and the activities of superoxide dismutase (SOD), catalase (CAT), and glutathione (GSH), markedly increased in the testicular tissue after SAL treatment. In addition, our data also showed a marked down-regulated the expressions of p38 MAPK phosphorylation and up-regulation the protein expressions of ZO-1, Occludin, Claudin-11, N-cadherin, and Connexin-43 after BET administration compared with the diabetic group. In conclusion, these results demonstrated that BET exerts protective effects on diabetes-induced BTB dysfunction, which may be through regulating oxidative stress-mediated p38 MAPK pathways.

International audience; Inspired by the works of Dewar, Murty and Kotěšovec, we establish some useful theorems for asymptotic formulas. As an application, we obtain asymptotic formulas for the numbers of skew plane partitions and cylin-dric partitions. We prove that the order of the asymptotic formula for the skew plane partitions of fixed width depends only on the width of the region, not on the profile (the skew zone) itself, while this is not true for cylindric partitions.

Cu(II) heterogenized on sodium carboxymethyl cellulose (Na-CMC) has been thoroughly characterized by different techniques. Cu(II)-CMC has been applied for the first time in the homocoupling reaction of a variety of terminal alkynes. The catalyst furnished good to excellent yields of the desired products and could be reused six times without loss of catalytic activity. The Cu(II)-CMC catalysis protocol is a new efficient route to synthesize 1,3-diynes under mild conditions.

An efficient and green copper(II) acetylacetonate-catalyzed protocol for the Huisgen-click reaction in water at 100 °C has been established. The protocol was not only suitable for the reaction between organic azides and alkynes, but also suitable for one-pot three-component reaction among alkyl halides, NaN3 and alkynes.

Change mode and effects analysis (CMEA) is a powerful technique for measuring product flexibility toward future changes and diminishing the cost of redesign as well as shortening time to market. As a systematic methodology, it provides an in-depth view for the investigation of potential changes, causes, and effects in designs, products, and processes. Traditional CMEA determines the risk priorities of change modes by using change potential number, which requires the risk factors of design flexibility, occurrence, and readiness to be precisely evaluated. However, this is not always possible in real applications due to the uncertainty and subjectivity involved in the early design stages. It has been criticized much for its deficiencies in criteria weighting of the risk factors, change potential number calculation, and risk priorities determination of the change modes. This paper presents a systematic evaluation approach for determining a more rational rank of change modes by combining with the entropy weight method, rough number, and grey relational analysis. In this study, the entropy weight method is adopted to calculate the relative importance of risk factors. Rough number is presented to aggregate individual weights and preferences, and to manipulate the vagueness in the evaluation process. Then a rough number enhanced grey relational analysis is proposed to evaluate the risk ranking of change modes. Finally, a practical example is put forward to validate the performance of the proposed method. The result shows that the proposed change mode evaluation method can effectively overcome the shortcomings of traditional CMEA and strengthen the objectivity of product flexibility measurement.

This paper proposes a novel fractional transform, denoted as the fractional Krawtchouk transform (FrKT), a generalization of the Krawtchouk transform. The derivation of the FrKT uses the eigenvalue decomposition method. We determine the eigenvalues and the corresponding multiplicity of the Krawtchouk transform matrix. Moreover, the orthonormal eigenvectors of the transform matrix are derived. For validation purpose only and as a first illustration of the interest of FrKT, a watermarking example was chosen. Experimental results show that better watermark robustness and imperceptibility are achieved by adjusting the fractional orders in the FrKT.

The aging of hydraulic concrete structure is a highly complicated problem. To reasonably evaluate the aging situation of a long-term operating concrete sluice, the core samples are obtained by field sampling from the sluice piers and the mercury injection experiment is carried out in this paper. The main objectives of this experimental investigation are to analyze the pore structure characteristics of the different parts in core samples and discuss the concrete aging rule of hydraulic concrete structure. The experimental results show that the aging of the hydraulic concrete has a certain relationship with the evolution of the concrete pore structure. It is feasible to use the pore structure of concrete to express the concrete aging of the hydraulic structure. The research in this paper will provide a basis for further study on the aging mechanism of the hydraulic concrete structure.

The symmetric flying wing has a simple structure and a high lift-to-drag ratio. Due to its complicated surface design, the flow field flowing through its surface is also complex and variable, and the three-dimensional effect is obvious. In order to verify the effect of microsecond pulse plasma flow control on the symmetric flying wing, two different sizes of scaling models were selected. The discharge energy was analyzed, and the force and moment characteristics of the two flying wings and the particle image velocimetry (PIV) results on their surface flow field were compared to obtain the following conclusions. The microsecond pulse surface dielectric barrier discharge energy density is independent of the actuator length but increases with the actuation voltage. After actuation, the stall angle of attack of the small flying wing is delayed by 4&deg, the maximum lift coefficient is increased by 30.9%, and the drag coefficient can be reduced by 17.3%. After the large flying wing is actuated, the stall angle of attack is delayed by 4&deg, the maximum lift coefficient is increased by 15.1%, but the drag coefficient is increased. The test results of PIV in the flow field of different sections indicate that the stall separation on the surface of the symmetric flying wing starts first from the outer side, and then the separation area begins to appear on the inner side as the angle of attack increases.

Neonatal hypoxic-ischemic brain damage (HIBD) is a leading cause of death and perpetual neurological dysfunction in neonates. Vanillin (Van), a natural phenolic compound with neuroprotective properties, exerts neuroprotection on a gerbil model of global ischemia by inhibiting oxidative damage. This study aimed to explore the potential neuroprotective roles of Van in neonatal rats suffering from hypoxic-ischemic (HI). An HI model of 7-day-old SD rats was induced by left carotid artery ligation followed by exposure to 8% oxygen (balanced with nitrogen) for 2.5 h at 37 °C. At 48 h after intraperitoneal injection with Van (20, 40, and 80 mg/kg) or saline, neurobehavioral function, cerebral infract volume, brain water content, and histomorphological changes were performed to evaluate brain injury. Transmission electron microscopy and immunoglobulin G (IgG) staining were conducted to evaluate the integrity of the blood-brain barrier (BBB). The levels of oxidative stress and tight junction proteins, as well as the activities of matrix metalloproteinases (MMPs), were also determined in the ipsilateral hemisphere. Results showed that Van post-treatment significantly ameliorated early neurobehavioral deficits, decreased infarct volume and brain edema, as well as attenuated histopathologic injury and IgG extravasation. Furthermore, Van markedly increased the activities of endogenous antioxidant enzymes and decreased malondialdehyde content. Meanwhile, the activation of MMP-2 and MMP-9 induced by HI was partially blocked by Van. Finally, Van obviously increased the expression of ZO-1, Occludin, and Claudin-5 compared with the HI group. Collectively, Van can provide neuroprotective effects against neonatal HIBD possibly by attenuating oxidative damage and preserving BBB integrity.

Spermatogenic dysfunction is one of the major secondary complications of male diabetes. Salidroside (SAL) is the important active ingredients isolated from Herba Cistanche, which exhibits numerous pharmacological activities such as antioxidant, anti-diabetic, and anti-inflammatory effects. The present study was designed to determine whether SAL contributes to the recovery from spermatogenic dysfunction in streptozotocin (STZ) induced type-1 diabetic mice. SAL (25, 50, or 100 mg/kg) and Clomiphene citrate (CC, 5 mg/kg) were orally administered to male type-1 diabetic mice for 10 weeks. Testis tissues were collected for histopathological and biochemical analysis. Moreover, reproductive organ weight, sperm parameters, and testicular cell DNA damage were estimated. The results revealed that SAL significantly improved the weight of the reproductive organs, sperm parameters and testicular morphology to different degrees in type-1 diabetic mice. Furthermore, reactive oxygen species (ROS) and malondialdehyde (MDA) levels were significantly reduced, and the activities of superoxide dismutase (SOD), catalase (CAT), and glutathione (GSH), markedly increased in the testicular tissue after SAL treatment. In addition, our data also showed a marked downregulation the fluorescence expressions of p38 MAPK phosphorylation and upregulation the protein expressions of ZO-1, Occludin, Claudin-11 and N-cadherin after SAL administration (100 mg/kg) compared with the type-1 diabetic group. In conclusion, these results demonstrated that SAL exerts protective effects on type-1 diabetes-induced male spermatogenic dysfunction, which is likely mediated by inhibiting oxidative stress-mediated blood testis barrier damage.

The Euler numbers occur in the Taylor expansion of tan ⁡ ( x ) + sec ⁡ ( x ) \tan (x)+\sec (x) . Since Stieltjes, continued fractions and Hankel determinants of the even Euler numbers, on the one hand, of the odd Euler numbers, on the other hand, have been widely studied separately. However, no Hankel determinants of the (mixed) Euler numbers have been obtained. The reason for that is that some Hankel determinants of the Euler numbers are null. This implies that the Jacobi continued fraction of the Euler numbers does not exist. In the present paper, this obstacle is bypassed by using the Hankel continued fraction, instead of the J J -fraction. Consequently, an explicit formula for the Hankel determinants of the Euler numbers is being derived, as well as a full list of Hankel continued fractions and Hankel determinants involving Euler numbers. Finally, a new q q -analog of the Euler numbers E n ( q ) E_n(q) based on our continued fraction is proposed. We obtain an explicit formula for E n ( − 1 ) E_n(-1) and prove a conjecture by R. J. Mathar on these numbers.

Covariance matrices, known as symmetric positive definite (SPD) matrices, are usually regarded as points lying on Riemannian manifolds. We describe a new covariance descriptor, which could improve the discriminative learning ability of region covariance descriptor by taking into account the mean of feature vectors. Due to the specific geometry of Riemannian manifolds, classical learning methods cannot be directly used on it. In this paper, we propose a subspace projection framework for the classification task on Riemannian manifolds and give the mathematical derivation for it. It is different from the common technique used for Riemannian manifolds, which is to explicitly project the points from a Riemannian manifold onto Euclidean space based upon a linear hypothesis. Under the proposed framework, we define a Gaussian Radial Basis Function- (RBF-) based kernel with a Log-Euclidean Riemannian Metric (LERM) to embed a Riemannian manifold into a high-dimensional Reproducing Kernel Hilbert Space (RKHS) and then project it onto a subspace of the RKHS. Finally, a variant of Linear Discriminative Analyze (LDA) is recast onto the subspace. Experiments demonstrate the considerable effectiveness of the mixed region covariance descriptor and the proposed method.

Objective: To explore the effect of preemptive analgesia (PA) with parecoxib sodium on the inflammatory cytokine and stress in puerpera after cesarean section. Methods: A total of 70 pregnant women who were admitted in our hospital from May, 2015 to May, 2016 for cesarean section were included in the study and randomized into the observation group and the control group with 35 cases in each group. A venous channel was established. The heart rate, blood pressure, and oxygen saturation were continuously monitored by the monitor. The patients in the observation group were intravenously injected with parecoxib sodium (40 mg) and normal saline (2 mL), while the patients in the control group were intravenously injected with normal saline (2 mL) 30 min before anesthesia induction. The venous blood when entering the operation room, after operation, 4 h, 8 h, and 12 h after operation was extracted. The plasma IL-6, TNF-α, P substance, E, and NE levels were detected. Results: IL-6 and TNF-α levels after operation in the two groups were elevated, reached the peak 4 h after operation, and were gradually reduced 8 h after operation. IL-6 and TNF-α levels at each timing point after operation in the observation group were significantly lower than those in the control group (P

As a class of semi-supervised learning methods, manifold regularization learning has recently attracted a lot of attention, due to their great success in exploiting the underlying geometric structures among data. This paper presents a novel semi-supervised approach by combining manifold regularization learning with the idea of multiple kernels, named after ensemble multiple-kernel manifold regularization learning. In our approach, multiple kernels we introduced are not only used to add the flexibility and diversity of the candidate space for the learning problem, but also act as a similarity measure to search for an optimal graph Laplacian in some sense. In other words, the proposed method allows us to learn an 'ideal' kernel and an optimal graph Laplacian simultaneously, which is of significant difference from existing methods. The associated optimization problem is solved efficiently by an alternating iteration procedure. We implement experiments over four real world data sets to demonstrate the benefits of the proposed method.

The health of wetland ecosphere in an estuarine delta is determined by many factors, such as continuity of natural processes, ecosystem connectivity, habitat heterogeneity, and food web diversity. The contradiction between ecological and environmental protection and regional development in the estuarine delta is becoming more and more prominent. A series of man-made and natural processes directly and indirectly resulted in habitat fragmentation of wetlands, which has direct and strong impacts on the ecosphere health and the habitat function of wetlands. In this paper, we provided a perspective on researches on the basic theory of healthy wetland ecosphere, landscape ecological network system, hydrologic network construction, key food webs, and habitat heterogeneity. At the regional and landscape scales, with the linkages between land use and ecosystem integrity as the main line, we clarified the influences of habitat fragmentation on wetland ecological functions, especially the effects of landscape integrity and river connectivity on wetland habitat. At the community and ecosystem scales, emphasis should be given on the relationship between food web and ecosystem stability, especially the supporting role of food web diversity and habitat heterogeneity on the construction of wetland biosphere. Further efforts should focuse on the wetland habitats construction based on landscape integrity, hydrologic connectivity, habitat heterogeneity and food web diversity. These efforts could help to develop and optimize the theory and method of constructing wetland ecosphere and enhancing its ecological function, and promote the sound development of regional ecological environment and resource utilization in estuarine deltas.河口三角洲湿地生态环境保护和区域开发的矛盾突出,对湿地生态圈健康和栖息地生态功能产生直接而强烈的影响.健康的河口三角洲湿地生态圈是由自然过程的连续性、生态系统的连通性、生境的异质性以及食物网的多样性等多种因素共同决定的.本文讨论了健康湿地生态圈构建的基础理论,综述了景观生态网络构建、水文连通性网络构建、食物网构建以及生境异质性栖息地营建的理论与方法.在区域和景观尺度上,以土地利用-生态系统完整性为主线,阐明了湿地破碎化对湿地生态功能的影响,特别强调景观完整性、水文连通性对湿地栖息地的影响;在生态系统和群落尺度上,以食物网-生态系统稳定性为主线,强调食物网多样性、生境异质性对湿地生物圈构建的支撑作用.基于景观完整性、水文连通性、生境异质性和食物网多样性构建健康湿地生态圈,可为湿地生态环境保护和建设提供科学依据和技术支撑.

Riemannian manifold recently has widely exploited in pattern recognition, data analysis, and machine learning. In this paper, a novel kernel learning method, based on preserving geodesic distance on Riemannian manifold, is proposed. In our approach, the features of data first are extracted by an covariance descriptor, and represented as covariance matrices (SPD matrices). Then an logarithm operation is used to transfer them to column vectors. Different from general doing, we introduce a parameterized Mahalanobis distance to define the distance between two column vectors, aiming to make it equal to the geodetic distance between two corresponding data on Riemannian manifold. Furthermore, an initialization kernel matrix is obtained from the learned Mahalanobis distance matrix by a linear transformation, and with it the Bregman optimization algorithm is applied to find the optimal kernel matrix, in which the distance in kernel space is equal to the geodetic distance on Riemannian manifold. We implement experiments on texture data sets to demonstrate the benefits of the proposed method.

An integrated rough number based method is presented to evaluate design concepts under subjective environment.Rough number is introduced to deal with the vagueness in decision-making.A novel AHP based on rough number is presented to determine the weight of each evaluation criterion.A rough number based VIKOR is proposed to evaluate the design concept alternatives.The proposed method can effectively enhance the objectivity in design concept evaluation. Design concept evaluation at the early stage of product design has been widely recognized as one of the most critical phases in new product development as it determines the direction of the downstream design activities. However, the information at this stage is mainly subjective and imprecise which only depends on experts' judgments. How to handle the vagueness and subjectivity in design concept evaluation becomes a critical issue. This paper presents a systematic evaluation method by integrating rough number based analytic hierarchy process (AHP) and rough number based compromise ranking method (also known as VIKOR) to evaluate design concepts under subjective environment. In this study, rough number is introduced to aggregate individual judgments and preferences and deal with the vagueness in decision-making. A novel AHP based on rough number is presented to determine the weight of each evaluation criterion. Then an improved rough number based VIKOR is proposed to evaluate the design concept alternatives. Sensitivity analysis is conducted to measure the impact of the decision makers' risk to the final evaluation results. Finally, a practical example is put forward to validate the performance of the proposed method. The result shows that the proposed decision-making method can effectively enhance the objectivity in design concept evaluation under subjective environment.

This paper focuses on a generic paradigm for quantitative behavioral knowledge modeling. The goal is to support automated functional case adaptation with behavioral inputs rather than structure parameter assignments. Functional case is a kind of functional module, integrating functional knowledge, qualitative behavioral knowledge, quantitative behavioral knowledge, and flexible structure models to support multiple design stages in a “5R” case recycle. Behavior effect analysis has been proposed to analyze the roles of behavior variables and structure parameters in the function implementing process and to establish primary relationships between them. Behavioral constraint has been introduced for knowledge representing in detailed design of a functional case. Behavior constraint matrix is presented to guide construction of fully constrained behavioral constraint equations. Examples of functional case modeling and recycling have been demonstrated. The proposed method will benefit designers in reuse of a functional case for a rapid design response in detailed design phase. Automated functional case adaption is achievable, which is especially significant for unskilled designers.

The irrationality exponent of an irrational number $\xi$, which measures the approximation rate of $\xi$ by rationals, is in general extremely difficult to compute explicitly, unless we know the continued fraction expansion of $\xi$. Results obtained so far are rather fragmentary, and often treated case by case. In this work, we shall unify all the known results on the subject by showing that the irrationality exponents of large classes of automatic numbers and Mahler numbers (which are transcendental) are exactly equal to $2$. Our classes contain the Thue--Morse--Mahler numbers, the sum of the reciprocals of the Fermat numbers, the regular paperfolding numbers, which have been previously considered respectively by Bugeaud, Coons, and Guo, Wu and Wen, but also new classes such as the Stern numbers and so on. Among other ingredients, our proofs use results on Hankel determinants obtained recently by Han., Comment: International Mathematics Research Notices 2015

Feature selection and case organization are crucial steps in case-based reasoning (CBR), since the retrieval efficiency and accuracy even the success of the CBR system are heavily dependent on their quality. However, inappropriate feature selection and case selection together with ill-structured case organization may not only present a dilemma in case retrieval, but also greatly increase the case base. To obtain an efficient CBR system, selection of proper features and suitable cases with appropriate case organization are very important. This paper proposes a hybrid CBR system by introducing reduction technique in feature selection and cluster analysis in case organization. In this study, a minimal set of features is selected from the problem domain while redundant ones are reduced through neighborhood rough set algorithm. Once feature selection is finished, the growing hierarchical self-organizing map (GHSOM) is taken as a cluster tool to organize those cases so that the initial case base can be divided into some small subsets with hierarchical structure. New case is led into corresponding subset for case retrieval. Experiments on UCI datasets and a practical case in electromotor product design show the effectiveness of the proposed approach. The results indicate that the research techniques can effectively enhance the performance of the CBR system.

International audience; The Hankel determinants of certain automatic sequences f are evaluated modulo a prime number. In most cases, the Hankel determinants of automatic sequences do not have any closed-form expressions; the traditional methods, such as LU-decomposition and Jacobi continued fraction, cannot be applied directly. Our method is based on a simple idea: the Hankel determinants of each sequence g equal to f modulo p are equal to the Hankel determinants of f modulo p. The clue then consists of finding a nice sequence g, whose Hankel determinants have closed-form expressions. Several examples are presented, including a result saying that the Hankel determinants of the Thue–Morse sequence are nonzero, first proved by Allouche, Peyrière, Wen and Wen using determinant manipulation.

An efficient protocol for the CuAAC reaction catalyzed by metallic copper wire for the synthesis of 1,4-disubstituted triazoles has been developed in supercritical carbon dioxide (scCO2) at 50 °C. The protocol could afford the corresponding products in excellent yields with a very easy work-up procedure. The metallic copper wire could be reused for more than 200 runs without decreasing the catalytic efficiency.

The concept of $t$-difference operator for functions of partitions is introduced to prove a generalization of Stanley's theorem on polynomiality of Plancherel averages of symmetric functions related to contents and hook lengths. Our extension uses a generalization of the notion of Plancherel measure, based on walks in the Young lattice with steps given by the addition of $t$-hooks. It is well-known that the hook lengths of multiples of $t$ can be characterized by the Littlewood decomposition. Our study gives some further information on the contents and hook lengths of other congruence classes modulo $t$., Comment: 24 pages

We prove that a family of average weights for oscillating tableaux are polynomials in two variables, namely, the length of the oscillating tableau and the size of the ending partition, which generalizes a result of Hopkins and Zhang. Several explicit and asymptotic formulas for the average weights are also derived., Comment: 12 pages