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In this paper, we investigate the Hyers–Ulam stability of the coefficient multipliers on the Hardy space H 2 and the Bergman space A 2 , meanwhile, we also investigate the Hyers–Ulam stability of the coefficient multipliers between the Bergman space A 2 and the Hardy space H 2 . We give the necessary and sufficient condition for the coefficient multipliers to have the Hyers–Ulam stability on the Hardy space H 2 , on the Bergman space A 2 and between the Bergman space A 2 and the Hardy space H 2 , respectively. We also show that the best constant of Hyers–Ulam stability exists under different circumstances. Some results generalized the results of MacGregor and Zhu when p = 2 in MacGregor and Zhu article (Mathematika 42:413–426, 1995). Moreover, some illustrative examples are also discussed. [ABSTRACT FROM AUTHOR]

The higher-order modified Korteweg–de Vries (mKdV) equation with constants background is revealed based on the Riemann–Hilbert problem (RHP). With the derivation of RHP, the one-soliton solution (oSS) and simple breather solution (sBS) of the higher-order mKdV equation are obtained for the first time. In addition, the dynamic behavior of the oSS and sBS were further discussed by some corresponding graphs with selecting appropriate parameters, which have not been studied in published works. [ABSTRACT FROM AUTHOR]

The inverse scattering of a higher-order nonlinear Schrödinger equation for inhomogeneous Heisenberg ferromagnetic system with zero boundary condition is calculated by an appropriate Riemann–Hilbert (RH) problem. The RH problem of reflection coefficient with multiple high-order poles is obtained. Meanwhile, the calculation formulas of bound-state (BS) solitons and multiple BS solitons corresponding to one high-order pole and multiple high-order poles are also calculated, respectively. Finally, the corresponding soliton solution model is calculated according to the corresponding formula. Simultaneously, we also obtain the BS soliton, the multiple BS soliton and the interaction between multiple BS solitons and multiple BS solitons. [ABSTRACT FROM AUTHOR]

Although TRPV1 channels represent a key player of noxious heat sensation, the precise mechanisms for thermal hyperalgesia remain unknown. We report here that conditional knockout of deSUMOylation enzyme, SENP1, in mouse dorsal root ganglion (DRG) neurons exacerbated thermal hyperalgesia in both carrageenan- and Complete Freund’s adjuvant-induced inflammation models. TRPV1 is SUMOylated at a C-terminal Lys residue (K822), which specifically enhances the channel sensitivity to stimulation by heat, but not capsaicin, protons or voltage. TRPV1 SUMOylation is decreased by SENP1 but upregulated upon peripheral inflammation. More importantly, the reduced ability of TRPV1 knockout mice to develop inflammatory thermal hyperalgesia was rescued by viral infection of lumbar 3/4 DRG neurons of wild-type TRPV1, but not its SUMOylation-deficient mutant, K822R. These data suggest that TRPV1 SUMOylation is essential for the development of inflammatory thermal hyperalgesia, through a mechanism that involves sensitization of the channel response specifically to thermal stimulation. [ABSTRACT FROM AUTHOR]

A series of (SiO/MgO/ID/MgCl)·TiCl Ziegler-Natta catalysts for propylene polymerization has been prepared with a new method. These catalysts were synthesized using soluble Mg-compounds as the Mg-source and the preparation progress was relatively simple. The catalyst could copy the spherical shape of the carrier very well. The propylene polymerization results showed that the catalyst revealed the best activity with 9,9-di(methoxymethyl)fluorene (BMMF) as internal donor at 50 °C with the optimal molar ratio Al/Ti = 5, which was much lower than what the industrial polypropylene catalyst used (at least molar ratio Al/Ti = 100), resulting in great cost saving. Additionally, the polymerization kinetics of the catalyst exhibited very stable property after achieving a relatively high value. These catalysts possessed rather high activity and good hydrogen response. The isotactic index (II.) value of the PP products could be higher than 98% in the presence of both internal and external electron donors. Moreover, temperature rising elution fractionation method was used to understand the influence of donors and H on the properties of the PP products. [ABSTRACT FROM AUTHOR]

Using the fixed point method and the weakly Picard operator technique, we establish some abstract Ulam-Hyers stability results for operatorial equations in noncommutative metric spaces. [ABSTRACT FROM AUTHOR]

In recent years, the research on the domestic and international sports industry has made considerable achievements, but there are still some loopholes in the content, that is, there is still a vacancy in the comprehensive quantitative evaluation of the economic development of the sports industry, especially in the statistics of the output value of the sports industry, which lacks a comprehensive understanding of the economic development of the industry. In the state of dual demand research and application, it is still necessary to reveal the publicity and education of industrial scale, industrial structure, industrial function and industrial safety between people and industries, which is also a necessary way to develop the talent guarantee industry. In this work, we should establish an economic model related to the sports industry. It mainly applies the deep learning algorithm and data information mining technology. After allowing the extraction of information from the sports industry database, it is converted into an economic model of the sports industry. It uses scientific and efficient processing methods to analyze a large number of diverse data, in order to find the hidden laws and knowledge behind it. Therefore, this paper uses data mining technology to process and analyze the economic development data of sports industry in detail and conducts corresponding quantitative analysis according to the requirements of data development. Finally, this paper points out that the neural network in the deep learning algorithm has further training and learning on the economic data of the sports industry, which is convenient for the subsequent prediction of the economic development of the sports industry to make a greater breakthrough. [ABSTRACT FROM AUTHOR]

In this paper, we introduce a reproducing kernel method for solving nonlocal fractional boundary value problems with uncertainty. An algorithm for solving nonlocal fuzzy fractional boundary value problems is presented. The results from numerical examples show that the present method is simple and effective. [ABSTRACT FROM AUTHOR]

Various (SiO/MgO/MgCl)·TiCl Ziegler-Natta catalysts modified by the third metal elements were synthesized by the co-impregnation of water-soluble magnesium and the third metal salts. Several key factors including the electronegativity of the third metal elements, catalyst performances in ethylene homo-polymerization, ethylene/1-hexene copolymerization and hydrogen response were systematically investigated. Both the catalyst performance and the polymer properties are influenced by the introduction of the third metal elements. Compared with the unmodified (SiO/MgO/MgCl)·TiCl Ziegler-Natta catalyst, activity and 1-hexene incorporation are enhanced by the introduction of zirconium, vanadium, aluminum and chromium, while deteriorated by the addition of ferrum, nickel, molybdenum and tungsten. Correlations of the catalyst activities and 1-hexene incorporation ability with the electronegativity of the third metal elements are discovered. It is found that the lower electronegativity of the third metal elements leads to the catalyst with higher activity and higher α-olefin co-polymerization ability. The polyethylene produced by a nickel modified catalyst showed broad molecular weight distribution (MWD) and the lowest average molecular weight (MW), while by using a ferrum modified catalyst, the resulting polyethylene had the highest MW, reaching the ultra-high MW area. Vanadium and chromium modified catalysts demonstrated the best hydrogen response. [ABSTRACT FROM AUTHOR]

We study the weak decays of B(s) and Bc into D-wave heavy-light mesons, including J P = 2- (D(s)2, D'(s)2, B(s)2, B'(s)2) and 3- (D∗(s)3, B*(s)3) states. The weak decay hadronic matrix elements are obtained based on the instantaneous Bethe-Salpeter method. The branching ratios for the B decays are B[ B →D²eνe] = 1.1-0.3 +0.3 ×10-3, B[ B → D' 2eνe] = 4.1-0.8+0.9 × 10-4, and B[ B → D∗ 3e¯νe] = 1.0-0.2 +0.2 ×10-3, respectively. For the semi-electronic decays of Bs to Ds2, D's2, and D∗ s3, the corresponding branching ratios are 1.7-0.5 +0.5 ×10-3, 5.2-1.5+1.6×10-4, and 1.5-0.4 +0.4 ×10-3, respectively. The branching ratios of the semi-electronic decays of Bc to D-wave D mesons are in the order of 10-5. We also obtained the forward-backward asymmetry, angular spectra, and lepton momentum spectra. In particular the distribution of decay widths for the 2- states D2 and D'² varying along with mixing angle are presented. [ABSTRACT FROM AUTHOR]

In this paper, we investigate the Hyers-Ulam stability of the differential operators $$T_\lambda $$ and D on the weighted Hardy spaces $$H_\beta ^2$$ with the reproducing property. We obtain a necessary and sufficient condition in order that D is stable on $$H_\beta ^2$$ , and construct an example concerning the stability of $$T_\lambda $$ on $$H_\beta ^2$$ . Moreover, we also investigate the Hyers-Ulam stability of the partial differential operators $$D_i$$ on the several variables reproducing kernel space $$H_f^2(\mathbb {B}_d)$$ . [ABSTRACT FROM AUTHOR]

Using the fixed point method and the weakly Picard operator technique, we obtain some abstract Ulam-Hyers stability results of the initial value problem of fractional differential equations in quaternionic analysis. Sufficient conditions for the existence of solutions of the initial value problem are given by the application of the method of associated spaces. An example is provided to illustrate these results. [ABSTRACT FROM AUTHOR]

In this paper, we establish sufficient conditions for the existence of solutions for the initial value problem of fractional differential equations. We consider the initial value problem in the space of Helmholtz-type generalized regular functions in the sense of quaternionic analysis. The results are obtained by the application of the method of associated spaces and the fixed point theorem. An example is provide to illustrate results. [ABSTRACT FROM AUTHOR]

The aim of this paper is to study the stability of fractional differential equations in Hyers-Ulam sense. Namely, if we replace a given fractional differential equation by a fractional differential inequality, we ask when the solutions of the fractional differential inequality are close to the solutions of the strict differential equation. In this paper, we investigate the Hyers-Ulam stability of two types of fractional linear differential equations with Caputo fractional derivatives. We prove that the two types of fractional linear differential equations are Hyers-Ulam stable by applying the Laplace transform method. Finally, an example is given to illustrate the theoretical results. [ABSTRACT FROM AUTHOR]

By means of the modified CK's direct method, we give out the relationship between variable coefficients of the fifth-order KdV equation and the corresponding constant coefficient ones. At the same time, we have studied the generalized fifth-order KdV equation with constants coefficients using the Lie symmetry group methods. By applying the nonclassical symmetry method we found that the analyzed model does not admit supplementary, nonclassical type, symmetries. At last, we give some exact analytic solutions by using the power series method. [ABSTRACT FROM AUTHOR]

This paper addresses the potential Korteweg-de Vries equation. The singular 1-soliton solution is obtained by the aid of ansatz method. Subsequently, the $$G^{\prime }/G$$ -expansion method and the exp-function approach also gives a few more interesting solutions. Finally, the Lie symmetry analysis leads to another plethora of solution to the equation. These results are going to be extremely useful and applicable in applied mathematics and theoretical physics. [ABSTRACT FROM AUTHOR]

This paper is concerned with the time fractional Sharma-Tasso-Olver (FSTO) equation, Lie point symmetries of the FSTO equation with the Riemann-Liouville derivatives are considered. By using the Lie group analysis method, the invariance properties of the FSTO equation are investigated. In the sense of point symmetry, the vector fields of the FSTO equation are presented. And then, the symmetry reductions are provided. By making use of the obtained Lie point symmetries, it is shown that this equation can transform into a nonlinear ordinary differential equation of fractional order with the new independent variable ξ= xt. The derivative is an Erdélyi-Kober derivative depending on a parameter α. At last, by means of the sub-equation method, some exact and explicit solutions to the FSTO equation are given. [ABSTRACT FROM AUTHOR]

In this paper, complete geometric symmetry of extended quantum Zakharov–Kuznetsov (QZK) equation are investigated. All of the geometric vector fields for the new extended QZK equation are presented. At the same time, a plethora of exact solutions are obtained by the application of the group theorem. In addition, 1-soliton solution of the extended QZK equation with power law nonlinearity is obtained by the aid of traveling wave hypothesis with the necessary constraints in place for the existence of the soliton. [ABSTRACT FROM AUTHOR]

Under the seller’s quantity discount, buyers self-organize or rely on a third party to aggregate their purchasing quantities to obtain lower prices. Because of the unequal member contributions in the cooperative purchasing organization, the buyers’ strategy is different, the members often fluctuate, and the organizations do not sustain themselves. An effective mechanism is necessary to improve the performance of purchasing groups. We study the various forms of cost allocation mechanism in practice. Different allocation rules may have influence on the buyers’ behavior (i.e., purchasing quantities, whether joining the organization or not). We analyze the serial cost allocation and equilibrium purchasing quantity based on a Nash equilibrium, and the results show that each buyer is worse off when not participating in the existence buying organization of the other buyers. We further find that the serial mechanism just confirms the most efficient Nash equilibrium: reasonable cost allocation rule is necessary for the subjects to identify their optimal strategy. [ABSTRACT FROM AUTHOR]

HOXA1 overexpression is sufficient for malignant transformation of nontumorigenic epithelial cells. It is known that HOXA1, which was upregulated in squamous cell carcinomas, affects both cell growth and death. The forced expression of HOXA1 in human breast cancer cells results in increased cell growth activity. However, it has not been reported in hepatocellular carcinoma (HCC). In this study, we used immunohistochemistry to compare HOXA1 protein expression in HCC and normal liver tissues and further analyzed HOXA1 protein expression in 156 clinicopathologically characterized HCC cases. We stably knocked down the endogenous expression level of HOXA1 in HepG2 cells with specific shRNA-expressing lentiviral vector. Following the successful establishment of stable cells, we examined in vitro cell growth by the MTT assay, anchorage-independent growth through a soft agar colony formation assay and cell migration/invasion by transwell and Boyden chamber assay. In addition, we also investigated in vivo tumor growth by xenograft transplantation of HepG2 cells into nude mice. Our results showed that the protein expression level of HOXA1 was markedly higher in HCC tissues than that in normal liver tissue ( P = 0.019). In addition, a high expression level of HOXA1 protein was positively correlated with the T classification ( P < 0.001), the N classification ( P < 0.001), distant metastasis ( P = 0.004), and the clinical stage ( P < 0.001) of HCC patients. Patients with higher HOXA1 expression showed a significantly shorter overall survival time compared with patients with low HOXA1 expression. Multivariate analysis suggested that HOXA1 expression might be an independent prognostic indicator ( P < 0.001) for the survival of patients with HCC. HOXA1-specific shRNA (shHOXA1) successfully knocked down HOXA1 endogenous expression in HepG2 cells. Compared to the parental and control shRNA-transfected (shCtrl) HepG2 cells, the shHOXA1 cells exhibited significantly reduced in vitro cell growth, anchorage-independent growth, and cell migration and invasion ( P < 0.05). In vivo, the xenograft transplants from shHOXA1 cells gave rise to much smaller tumors compared with those from shCtrl cells. Collectively, high HOXA1 expression is associated with poor overall survival in patients with HCC. The downregulation of HOXA1 inhibits growth, anchorage-independent growth, and migration and invasion of HepG2 cells. [ABSTRACT FROM AUTHOR]

In this paper, we determine the general solution of the functional equation f (kx+ y)+ f (kx-y) = g(x+y)+g(x-y)+h(x)+h(y) for fixed integers k with k ≠= 0,±1 without assuming any regularity condition on the unknown functions f ,g,h,h. The method used for solving these functional equations is elementary but exploits an important result due to Hosszú. The solution of this functional equation can also be determined in certain type of groups using two important results due to Székelyhidi. The results improve and extend some recent results. [ABSTRACT FROM AUTHOR]

The aim of this study was to investigate the expression and prognostic significance of RIN1 in gastric adenocarcinoma. RIN1 expression was analyzed using quantitative real-time PCR (qRT-PCR), Western blotting, and immunohistochemical staining on tissue samples from a consecutive series of 315 gastric adenocarcinoma patients who underwent tumor resections between 2003 and 2006. The relationship between RIN1 expression, clinicopathological factors, and patient survival was investigated. qRT-PCR results showed that the RIN1 mRNA expression was higher in tumor tissue samples than in the adjacent normal tissues, and a corresponding increase in protein expression was confirmed by Western blotting. Immunohistochemical staining indicated that RIN1 is highly expressed in 54.3 % of gastric adenocarcinomas. RIN1 expression levels were closely associated with tumor size, histological differentiation, tumor stage, and lymph node involvement. Kaplan-Meier survival analysis showed that high RIN1 expression exhibited a significant correlation with poor prognosis for gastric adenocarcinoma patients. Multivariate analysis revealed that RIN1 expression is an independent prognostic parameter for the overall survival rate of gastric adenocarcinoma patients. Our data suggest that RIN1 plays an important role in gastric adenocarcinoma progression and that a high RIN1 expression predicts an unfavorable prognosis in gastric adenocarcinoma patients. [ABSTRACT FROM AUTHOR]

With the growing popularity of 3G-powered devices, there are growing demands on energy-efficient data transmission strategies for various embedded systems. Different from the past work in energy-efficient real-time task scheduling, we explore strategies to maximize the amount of data transmitted by a 3G module under a given battery capacity. In particular, we present algorithms under different workload configurations with and without timing constraint considerations. Experiments were then conducted to verify the validity of the strategies and develop insights in energy-efficient data transmission. [ABSTRACT FROM AUTHOR]

274-bp conserved fragment of chiA ( chiA -CF) was amplified from the genomic DNA of Isoptericola jiangsuensis CLG (DSM 21863, CCTCC AB208287) using the specific PCR primers. Based on chiA-CF sequences, a 5233-bp DNA fragment was obtained by self-formed adaptor PCR. DNA sequencing analysis revealed there were two contiguous open reading frames coding for the precursors of Is -chiA [871 amino acids (aa)] and Is-chiB (561 aa) in the 5233-bp DNA fragment. The Is-chiA and Is-chiB exhibited 58% and 62% identity with ArChiA and ArChiB chitinase from Arthrobacter sp. TAD20, respectively. The Is-chiA and Is-chiB genes were cloned into expression vector pET28a (+) and expressed in Escherichia coli BL21 (DE3) with isopropyl-β- d-thiogalactopyranoside induction. Is-chiA and Is-chiB were 92 kDa and 60 kDa by sodium dodecyl sulfate-polyacrylamide gel electrophoresis and showed chitobiosidase and endochitinase activity, respectively. Is-chiA and Is-chiB were purified by Ni-nitrilotriacetic acid affinity chromatography and the characteristics of both Is-chiA and Is-chiB were studied. [ABSTRACT FROM AUTHOR]

We prove the generalized Hyers-Ulam stability of the following additive-cubic equation f(kx + y) + f(kx - y) = kf(x + y) + kf(x - y) + 2f(kx) - 2kf(x) in the setting of random normed spaces. [ABSTRACT FROM AUTHOR]

We achieve the general solution of the quintic functional equation f(x + 3y) - 5f(x + 2y) + 10f(x + y) - 10f(x) + 5f(x - y) - f(x - 2y) = 120f(y) and the sextic functional equation f(x + 3y) - 6f(x + 2y) + 15f(x + y) - 20f(x) + 15f(x - y) - 6f(x - 2y) + f(x - 3y) = 720f(y). Moreover, we prove the stability of the quintic and sextic functional equations in quasi-β-normed spaces via fixed point method. [ABSTRACT FROM AUTHOR]

In the prediction process of large-scale earthquake damage occurred in urban and rural regions, new models and approaches, which are different from traditional ones, should be adopted to rapidly predict earthquake damage. This article utilizes sampled population and buildings data that is easily available from the statistical database to conduct vulnerability analysis of buildings on the basis of earthquake damage of existing urban buildings in an analogical way, so as to provide a relation model between population data and disaster losses. In virtue of this model, the average vulnerability matrix of buildings of different structures in Fujian Province is established, the matrix adjustment coefficient of different decades is developed in accordance with the economic conditions, and the rapid evaluation system is set up as well. The result shows: this evaluation model, based on the population statistical data has merits as small investment, automatic data prediction, regular updates, as well as the advantage of easy accessibility. [ABSTRACT FROM AUTHOR]

Classical software configuration management which deals with source code versioning becomes insufficient when most components are distributed in binary form. As an important aspect of software configuration, protocol configuration also encounters those problems. This paper focuses on solving protocol component versioning issues for protocol configuration management on embedded system, incorporating the following versioning issues: version identification, version description and protocol component archiving and retrieving based on the version library. [ABSTRACT FROM AUTHOR]

The mass of the embedded systems are driven by second batteries, not by wired power supply. So saving energy is one of the main design goals for embedded system. In this paper we present a new technique for modelling and solving the dynamic power management (DPM) problem for embedded systems with complex behavioural characteristics. First we model a power-managed embedded computing system as a controllable Flow Chart. Then we use the Poisson process for optimisation, and give the power management algorithm by the help of Dynamic Voltage Scaling (DVS) technology. At last we built the experimental model using the PXA 255 Processors. The experimental results showed that the proposed technique can achieve more than 12% power saving compared to other existing DPM techniques. [ABSTRACT FROM AUTHOR]

For increased and various communication requirements of modern applications on embedded systems, general purpose protocol stacks and protocol models are not efficient because they are fixed to execute in the static mode. We present the Component-Based Communication Protocol Architecture (CCPA) to make communication dynamic and configurable. It can develop, test and store the customized components for flexible reuse. The protocols are implemented by component assembly and support by configurable environments. This leads to smaller memory, more flexibility, more reconfiguration ability, better concurrency, and multiple data channel support. [ABSTRACT FROM AUTHOR]

In this paper, using Brzdȩk and Ciepliński's fixed point theorems in a 2-Banach space, we investigate approximate solution for the generalized inhomogeneous radical quadratic functional equation of the form f(ax2+by2)=af(x)+bf(y)+D(x,y), where f is a mapping on the set of real numbers, a,b∈R+ and D(x,y) is a given function. Some stability and hyperstability properties are presented. [ABSTRACT FROM AUTHOR]