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In this paper, by introducing some parameters and using the way of weight function, a new integral inequality with a best constant factor is given, which is a relation between Hilbert's integral inequality and a Hilbert-type inequality. As applications, the equivalent form, the reverse forms and some particular inequalities are considered.

In this paper, by using the way of weight function and the technic of real analysis, a new integral inequality with some parameters and a best constant factor is given, which is a relation to two basic Hilbert-type integral inequalities. The equivalent form and the reverse forms are considered.

Self-incompatibility (SI) in Lolium perenne is controlled gametophytically by the S-Z two-locus system. S and Z loci mapped to L. perenne linkage groups 1 and 2, respectively, with their corresponding putative-syntenic regions on rice chromosome 5 (R5) and R4. None of the gene products of S and Z have yet been identified. SI cDNA libraries were developed to enrich for SI expressed genes in L. perenne. Transcripts were identified from the SI libraries that were orthologous to sequences on rice R4 and R5. These represent potential SI candidate genes. Altogether ten expressed SI candidate genes were identified. A rapid increase in gene expression within two minutes after pollen-stigma contact was revealed, reaching a maximum between 2 and 10 min. The potential involvement of these genes in the SI reactions is discussed.

In this work, by introducing some parameters and estimating the weight coefficient, a new inequality with a best constant factor is established, which is a relation between Hilbert’s inequality and a Hilbert-type inequality. As applications, the reverse form and some particular results are considered.

In this paper, by introducing some parameters and estimating the weight function, we give a new Hilbert-type integral inequality with a best constant factor. The equivalent inequality and the reverse forms are considered.

Byintroducing someparameters andthe weight coefficient, oneproves anewextension of the Hilbert-type inequality with a best constant factor. The reverse, some equivalent forms and a number of new particular cases are considered.

By using the improved Euler-Maclaurin’s summation formula, a more accurate Hilbert’s type inequality is built. As applications, the equivalent form is considered. All the lemmas and the theorem provide some new estimates on this type of inequalities. Mathematics Subject Classification: 26D15

In this paper, a new Hardy-type integral inequality with a best constant factor is considered. Mathematics Subject Classifications: 26D15

By using the way of real analysis and estimating the weight functions, we build a new Hilbert-type integral inequality in the whole plane with a non-homogeneous kernel and a few parameters. The constant factor related to the beta function is proved to be the best possible. We also consider the equivalent forms, the reverses, and some particular cases.

OBJECTIVE To delineate a deletional mutation of the Dystrophin gene on the short arm of chromosome X in a family affected with Duchenne/Becker muscular dystrophy. METHODS G-banded karyotyping, multiple ligation probe amplification (MLPA), array-based comparative genomic hybridization(array-CGH) and whole genome exon high-throughput sequencing were employed to delineate the mutation in the family. RESULTS GTG banding has demonstrated deletion of the terminal part of the short arm of chromosome X in the fetus. The same deletion was also found in its mother and maternal grandmother. MLPA analysis has revealed removal of exons 52 to 79 of the Dystrophin gene. A 30 Mb deletion in Xp22.33-p21.1 and a 10 Mb duplication in Xq27.2-q28 were identified by array-CGH and whole genome exon high-throughput sequencing. CONCLUSION The Xp deletion has led to deletion of exons 52 to 79 of the Dystrophin gene in the family. The female carriers also had certain features of Turner syndrome due to the same deletion.

Hilbert-type inequalities are divided three parts: Hilbert’s inequalities (1908), Hardy-Hilbert-type inequalities (1934) and Yang-Hilbert-type inequalities (2009). In this paper, we give a summary of the development of the theory of Hilbert-type inequalities during the past 110 years.

BackgroundCharacterization of genetic variations in maize has been challenging, mainly due to deterioration of collinearity between individual genomes in the species. An international consortium of maize research groups combined resources to develop the maize haplotype version 3 (HapMap 3), built from whole genome sequencing data from 1,218 maize lines, covering pre-domestication and domesticated Zea mays varieties across the world.ResultsA new computational pipeline was set up to process over 12 trillion bp of sequencing data, and a set of population genetics filters were applied to identify over 83 million variant sites.ConclusionsWe identified polymorphisms in regions where collinearity is largely preserved in the maize species. However, the fact that the B73 genome used as the reference only represents a fraction of all haplotypes is still an important limiting factor.

By applying the method of weight functions and the technique of real analysis, a multidimensional Hilbert-type integral inequality with multi-parameters and the best possible constant factor related to the gamma function is given. The equivalent forms and the reverses are obtained. We also consider the operator expressions and a few particular results related to the kernels of non-homogeneous and homogeneous.

By introducing a mixed kernel function and the proper parameters, a new Hilbert-type integral inequality with a best constant factor in the whole plane is derived. As an application, the operator expressions, reverse inequalities, and Hardy-type inequalities are considered.

By applying the way of real and functional analysis and estimating the weight functions, we build some lemmas and deduce some Hilbert-type and Hilbert-Hardy-type integral inequalities with the best possible constant factors. The equivalent forms, the reverses and the operator expressions are all considered. The composition formula of two Hilbert-Hardy-type integral operators and some examples are given.

This work is concerned with the existence and uniqueness of weighted Stepanov-like pseudo-almost automorphic mild solutions for a class of semilinear fractional differential equations, $D_{t}^{\alpha}x(t)=Ax(t)+D_{t}^{\alpha-1}F(t,x(t))$ , $t\in \mathbb{R}$ , where $1

ON THE NORM OF A LINEAR OPERATOR AND ITS APPLICATIONS

By the way of using real analysis and estimating the weight functions, two kinds of Hilbert-type integral inequalities in the whole plane with a non-homogeneous kernel and a homogeneous kernel are given. The constant factor related to the triangle functions is proved to be the best possible. We also consider the equivalent forms, the reverses, some particular cases, and two kinds of operator expressions.

Applying methods of Real Analysis and Functional Analysis, we build two weight functions with parameters and provide two kinds of parameterized Yang–Hilbert-type integral inequalities with the best constant factors. Equivalent forms, the reverses, and the operator expressions are also given. In particular, the Hardy-type inequalities and Hardy-type operators are studied. Additionally, a number of examples with two kinds of particular kernels are considered.

In this paper, the expression of the norm of a self-adjoint integral operator T : L 2(0,∞) → L 2(0,∞) is obtained. As applications, a new bilinear integral inequality with a best constant factor is established and some particular cases are considered.

Plastic deformation and dynamic recrystallization (DRX) behaviors of magnesium alloy AZ31B during thermal compression and extrusion processes were studied. In addition, effects of deformation temperature and rates on the microstructure and mechanical properties were investigated. The results show that the DRX grains nucleate initially at the primary grain boundaries and the twin boundaries, and the twinning plays an important role in the grain refinement. The DRX grain size depends on the deformation temperature and strain rate The average grain size is only 1 μm when the strain rate is 5 s−1 and temperature is 250 °C. It is also found that the DRX grain can grow up quickly at the elevated temperature. The microstructure of extruded rods was consisted of tiny equal-axis DRX grains and some elongated grains. The rods extruded slowly have tiny grains and exhibit good mechanical properties.

In this paper, the norm of an integral operator T : L r ( 0 , ∞ ) → L r ( 0 , ∞ ) ( r > 1 ) is obtained. As applications, a new bilinear integral operator inequality with the norm and the equivalent forms are given, and some new Hilbert's type inequalities with the best constant factors as the particular cases are established.

By introducing some parameters and estimating the weight coefficient, we give a new extension of Hilbert’s inequality with a best constant factor, which involves the β function. As its applications, we consider the equivalent form and some particular results.

This paper deals with a dual Hardy-Hilbert’s inequality with a best constant factor involving the beta function, which is an extension of the Hilbert’s inequality with the form of (p,q)-parameter. We also consider its extended form and an equivalent inequality.

In this paper, by using the Euler-Maclaurin’s summation formula, and estimating the weight coefficient, we give a new extension of Hilbert’s double series theorem with (p, q) - parameter and λ e (0, 4] , which involves the β function as a best constant factor. As applications, we consider the equivalent form and some particular results.

This paper deals with a new extension of Hilbert’s inequality with a (p, q)− parameter and a best constant factor. We also consider a more extended form and the equivalent inequality. Mathematics subject classification (2000): 26D15.

Using a fixed-point theorem in cone, existence criteria are proved for the periodic positive solutions of a delay differential equation with piecewise constant arguments. Several examples concerning biological models for the survival of red blood cells are given.

By introducing three parameters A, B and α, and estimating the weight coefficient, we give a new extension of Hilbert's inequality with a best constant factor involving the β function. As applications, we consider the equivalent form and some particular results.

This paper deals with a new Hardy-Hilbert’s type inequality with a best constant factor. As applications, we give its equivalent form and some particular results. Mathematics subject classification (2000): 26D15.

The Hilbert-type inequalities are certain significant weight inequalities, which play an important role in mathematical analysis and its applications. In this paper, we introduce the way of weight coefficient and consider its applications to the Hilbert-type inequalities. We will summarize how to use the way of weight coefficient to obtain some new improvements and generalizations of the Hilbert-type inequalities. Mathematics subject classification (2000): 26D15.

In this paper, by introducing three parameters A , B , and λ , and estimating the weight coefficient, we give a generalization of the extended Hardy–Hilbert's inequality with a best possible constant factor, involving the β function. We also consider its equivalent inequality and the associated double series form.

In this paper, the existence of positive, radially symmetric entire solutions for the equations @D^mu=f(|x|,u,|@?u|)(m=2,3,...) on R^2 is proved. Some properties of the solutions are obtained. The results of this paper are generalizations of these proved in [W. Water, Math. Z 67 (1957) 32-37; W. Water, Arch. Math 9 (1958) 308-312; W. Water, H. Rhee, Proc. Royal Soc. Edinburgh A 82 (1979) 189-192; T. Kusno, C.A. Swanson, Hiroshima Math. J. 17 (1989) 13-28].

By introducing three parameters A , B and λ , we give a generalization of Hilbert’s inequality with a best constant factor and some particular results. Mathematics subject classification (2000): 26D15.

Objective To present our experience in surgical management of urolithiasis in patients after urinary diversion. Patients and methods Twenty patients with urolithiasis after urinary diversion received intervention. Percutaneous nephrolithotomy, percutaneous based antegrade ureteroscopy with semi-rigid or flexible ureteroscope, transurethral reservoir lithotripsy, percutaneous pouch lithotripsy and open operation were performed in 8, 3, 2, 6, and 1 patients, respectively. The operative finding and complications were retrospectively collected and analyzed. Results The mean stone size was 4.5 ± 3.1 (range 1.5-11.2) cm. The mean operation time was 82.0 ± 11.5 (range 55-120) min. Eighteen patients were rendered stone free with a clearance of 90%. Complications occurred in 3 patients (15%). Two patients (10%) had postoperative fever greater than 38.5 °C, and one patient (5%) suffered urine extravasations from percutaneous tract. Conclusions The percutaneous based procedures, including percutaneous nephrolithotomy, antegrade ureteroscopy with semi-rigid ureteroscope or flexible ureteroscope from percutaneous tract, and percutaneous pouch lithotripsy, provides a direct and safe access to the target stones in patients after urinary diversion, and with high stone free rate and minor complications. The surgical management of urolithiasis in patients after urinary diversion requires comprehensive evaluation and individualized consideration depending upon the urinary diversion type, stone location, stone burden, available resource and surgeon experience.

β-Arrestin2 has been identified to act as a corepressor of androgen receptor (AR) signaling by binding to AR and serving as a scaffold to affect the activity and expression of AR in androgen-dependent prostate cancer cells; however, little is known regarding its role in castration-resistant prostate cancer (CRPC) progression. Here, our data demonstrated that β-arrestin2 contributes to the cell viability and proliferation of CRPC via the downregulation of FOXO1 activity and expression. Mechanistically, in addition to its requirement for FOXO1 phosphorylation induced by IGF-1, β-arrestin2 could inhibit FOXO1 activity in an Akt-independent manner and delay FOXO1 dephosphorylation through the inhibition of PP2A phosphatase activity and the attenuation of the interaction between FOXO1 and PP2A. Furthermore, β-arrestin2 could downregulate FOXO1 expression via ubiquitylation and proteasomal degradation. Together, our results identified a novel role for β-arrestin2 in the modulation of the CRPC progress through FOXO1. Thus, the characterization of β-arrestin2 may represent an alternative therapeutic target for CRPC treatment.

In this paper, by using the way of weight coefficients and technique of real analysis, a more accurate multidimensional discrete Mulholland-type inequality with the best possible constant factor is given, which is an extension of the Mulholland inequality. The equivalent form, the operator expression with the norm as well as a few particular cases are also considered.

By the use of the way of real analysis, we estimate the weight functions and give some new Hilbert-type integral inequalities in the whole plane with nonhomogeneous kernels and multiparameters. The constant factors related to the hypergeometric function and the beta function are proved to be the best possible. We also consider the equivalent forms, the reverses, and some particular cases in the homogeneous kernels.

In this chapter, using methods of weight functions and techniques of real analysis, we provide a multidimensional Hilbert-type integral inequality with a homogeneous kernel of degree 0 as well as a best possible constant factor related to the Riemann zeta function. Some equivalent representations and certain reverses are obtained. Furthermore, we also consider operator expressions with the norm and some particular results.