SOME COMPLETELY MONOTONIC FUNCTIONS ASSOCIATED WITH THE q-GAMMA AND THE q-POLYGAMMA FUNCTIONS

In this paper, the q-analogue of the Stirling formula for the q-gamma function （Moak formula） is exploited to prove the complete monotonicity properties of some functions involving the q-gamma and the q-polygamma functions for all real number q 〉 0. The monotonicity of these functions is used to establish sharp inequalities for the q-gamma and the q-polygamma functions and the q-Harmonic number. Our results are shown to be a generalization of results which were obtained by Selvi and Batir [23].

ON THE DEGREE OF COMPLETENESS OF CRYPTOGRAPHIC FUNCTIONS

This paper discusses the degree of completeness of cryptographic functions, which is one of the cryptographic criteria should be considered in the design of stream ciphers. We establish the relationships between the degree of completeness and other cryptographic criteria. For resilient Boolean functions, a method to enhance the degree of completeness is proposed, while the nonlinearity and the algebraic degree do not decrease. Moreover, two constructions of resilient functions are provided, which have optimal degree of completeness, high nonlinearity, and high algebraic degree.

Complete Monotonicity of Functions Related to Trigamma and Tetragamma Functions

In this paper,we study the completely monotonic property of two functions involving the functionΔ(x)=[ψ′(x)]2+ψ″(x)and deduce the double inequality x^(2)+3x+3/3x^(4)(2x+1)^(2)<Δ(x)<625x^(2)+2275x+5043/3x^(4)(50x+41)^(2),x>0which improve some recent results,whereψ(x)is the logarithmic derivative of the Gamma function.Also,we deduce the completely monotonic degree of a function involvingψ′(x).

COMPLETE MONOTONICITY FOR A NEW RATIO OF FINITELY MANY GAMMA FUNCTIONS

In this paper,by deriving an inequality involving the generating function of the Bernoulli numbers,the author introduces a new ratio of finitely many gamma functions,finds complete monotonicity of the second logarithmic derivative of the ratio,and simply reviews the complete monotonicity of several linear combinations of finitely many digamma or trigamma functions.

Construction and application of a three-dimensional vascular variation-based nephrometry scoring system for completely endophytic renal tumors

Background:Completely endophytic renal tumors(CERT)pose significant challenges due to their anatomical complexity and loss of visual clues about tumor location.A facile scoring model based on three-dimensional(3D)reconstructed images will assist in better assessing tumor location and vascular variations.Methods:In this retrospective study,80 patients diagnosed with CERT were included.Forty cases underwent preoperative assessment using 3D reconstructed imaging(3D-Cohort),while the remaining 40 cases were assessed using two-dimensional imaging(2D-Cohort).Vascular variations were evaluated by ascertaining the presence of renal arteries>1,prehilar branching arteries,and arteries anterior to veins.The proposed scoring system,termed RAL,encompassed three critical components:(R)adius(maximal tumor diameter in cm),(A)rtery(occurrence of arterial variations),and(L)ocation relative to the polar line.Comparison of the RAL scoring system was made with established nephrometry scoring systems.Results:A total of 48(60%)patients exhibited at least one vascular variation.In the 2D-Cohort,patients with vascular variations experienced significantly prolonged operation time,increased bleeding volume,and extended warm ischemia time compared with those without vascular variations.Conversely,the presence of vascular vari-ations did not significantly affect operative parameters in the 3D-Cohort.Furthermore,the 2D-Cohort demon-strated a notable decline in both short-and long-term estimated glomerular filtration rate(eGFR)changes com-pared with the 3D-Cohort,a trend consistent across patients with warm ischemia time≥25 min and those with vascular variations.Notably,the 2D-Cohort exhibited a larger margin of normal renal tissue compared with the 3D-Cohort.Elevated RAL scores correlated with larger tumor size,prolonged operation time,extended warm is-chemia time,and substantial postoperative eGFR decrease.The RAL scoring system displayed superior predictive capabilities in assessing postoperative eGFR changes compared with conventional nephrometry scoring systems.Conclusions:Our proposed 3D vascular variation-based nephrometry scoring system offers heightened proficiency in preoperative assessment,precise prediction of surgical complexity,and more accurate evaluation of postoper-ative renal function in CERT patients.

REFINEMENTS OF TRANSFORMATION INEQUALITIES FOR ZERO-BALANCED HYPERGEOMETRIC FUNCTIONS

In the article, we present some refinements of three classes of transformation inequalities for zero-balanced hypergeometric functions by use of the updated monotonicity criterion for the quotient of power series.

SOME DOUBLE SEQUENCE SPACES OF FUZZY NUMBERS DEFINED BY ORLICZ FUNCTIONS

In this article, we introduce some double sequence spaces of fuzzy real numbers defined by Orlicz function, study some of their properties like solidness, symmetricity, completeness etc, and prove some inclusion results.

The k Nearest Neighbors Estimator of the M-Regression in Functional Statistics

It is well known that the nonparametric estimation of the regression function is highly sensitive to the presence of even a small proportion of outliers in the data.To solve the problem of typical observations when the covariates of the nonparametric component are functional,the robust estimates for the regression parameter and regression operator are introduced.The main propose of the paper is to consider data-driven methods of selecting the number of neighbors in order to make the proposed processes fully automatic.We use thek Nearest Neighbors procedure(kNN)to construct the kernel estimator of the proposed robust model.Under some regularity conditions,we state consistency results for kNN functional estimators,which are uniform in the number of neighbors(UINN).Furthermore,a simulation study and an empirical application to a real data analysis of octane gasoline predictions are carried out to illustrate the higher predictive performances and the usefulness of the kNN approach.

Hermite interpolation and its numerical differentiation formula involving symmetric functions

By utilizing symmetric functions,this paper presents explicit representations for Hermite interpolation and its numerical differentiation formula.And the corresponding error estimates are also provided.

Study on the Improvement of the Application of Complete Ensemble Empirical Mode Decomposition with Adaptive Noise in Hydrology Based on RBFNN Data Extension Technology

The complex nonlinear and non-stationary features exhibited in hydrologic sequences make hydrological analysis and forecasting difficult.Currently,some hydrologists employ the complete ensemble empirical mode decomposition with adaptive noise(CEEMDAN)method,a new time-frequency analysis method based on the empirical mode decomposition(EMD)algorithm,to decompose non-stationary raw data in order to obtain relatively stationary components for further study.However,the endpoint effect in CEEMDAN is often neglected,which can lead to decomposition errors that reduce the accuracy of the research results.In this study,we processed an original runoff sequence using the radial basis function neural network(RBFNN)technique to obtain the extension sequence before utilizing CEEMDAN decomposition.Then,we compared the decomposition results of the original sequence,RBFNN extension sequence,and standard sequence to investigate the influence of the endpoint effect and RBFNN extension on the CEEMDAN method.The results indicated that the RBFNN extension technique effectively reduced the error of medium and low frequency components caused by the endpoint effect.At both ends of the components,the extension sequence more accurately reflected the true fluctuation characteristics and variation trends.These advances are of great significance to the subsequent study of hydrology.Therefore,the CEEMDAN method,combined with an appropriate extension of the original runoff series,can more precisely determine multi-time scale characteristics,and provide a credible basis for the analysis of hydrologic time series and hydrological forecasting.

Bowel function and quality of life after minimally invasive colectomy with D3 lymphadenectomy for right-sided colon adenocarcinoma

BACKGROUND Changes in bowel function after right-sided colectomy are not well understood compared to those associated with left-sided colectomy or rectal resection.In particular,there are concerns about bowel function after right-sided colectomy with complete mesocolic excision,which has become popular in the West.AIM To evaluate the functional outcomes of patients who underwent right-sided colectomy with D3 lymphadenectomy for colon cancer.METHODS Functional data from patients who underwent minimally invasive right-sided colectomy for colon cancer from October 2017 to September 2018 were prospectively collected.Functional outcomes were evaluated preoperatively and at 3,6,12,and 18 mo postoperatively.RESULTS Prior to surgery,57 patients answered the questionnaire,and 47 responded at three months,52 at 6 mo,52 at 12 mo,and 25 at 18 mo postoperatively.Most scales of quality of life and bowel function improved significantly over time.Urgency persisted to a high degree throughout the period without a significant change over time.The use of medications for defecation was about 10%over the entire period.Gas(P=0.023)and fecal frequency(P<0.001)increased,and bowel dysfunction group(P=0.028)was more common among patients taking medication.At six months,resected bowel and colon lengths were significantly different as a risk factor between the dysfunction group and the no dysfunction group[odd ratio(OR):1.095,P=0.026;OR:1.147,P=0.031,respectively]in univariate analysis,but not in multivariate analysis.CONCLUSION Despite D3 lymphadenectomy,most bowel symptoms improved over time after right-sided colectomy using a minimally invasive approach,and continuous medication was needed in only approximately 10%of patients.

Tumor recurrence after pathological complete response in locally advanced gastric cancer after neoadjuvant therapy:Two case reports

BACKGROUND The pathological complete response(ypCR)rate following neoadjuvant chemotherapy for advanced gastric cancer remains low and lacks a universally accepted treatment protocol.Immunotherapy has achieved breakthrough progress.CASE SUMMARY We report two female patients with gastric cancer defined as clinical stage cT4N1-2M0.Detection of mismatch repair protein showed mismatch repair function defect,and perioperative treatment with programmed death protein 1 inhibitor combined with S-1+oxaliplatin achieved ypCR.Surprisingly,the patients underwent clinical observation after surgery but developed different degrees of metastasis at~6 mo after surgery.CONCLUSION PD-1 inhibitor combined with chemotherapy provides a more strategic choice for comprehensive perioperative treatment of gastric cancer.

The Functional Gradient Description Method of Space Coordinate Transformation

The 3-dimension coordinate datum transformation is very important in geomatics.Generally,there are small angle coordinate transformation model (i.e.,Bursa model,et al) and large angle coordinate transformation model (i.e.,Rodrigo matrix model,et al).However,these papers only focus on the fixed and static situation regardless of the small or large angle.This paper proposes the conception of coordinate transformation gradient field,which can realize the space coordinate transformation from small angle to arbitrary angle,and from static to dynamical.Based on the equivalent characteristics of the unit quaternion rotation matrix and the Rodrigo matrix,through studying the mathematical relationship between the spatial coordinate transformation and the functional gradient,we derive a functional gradient expression of the arbitrary transformation formula in space.The study shows that the essence of spatial coordinate transformation is a kind of potential field mathematically.This potential field conception can unify all the space coordinate transformations.It is the theoretical foundation for the further study of time continuous space coordinate transformation,and this study gives a new solution for the attitude determination of motion carriers.

CHARACTERISTIC THEOREMS OF TH ENATURAL TCHEBYSHEFF SPLINE FUNCTION

In this paper,we give four characteristic theorems of the natural Tchebysheff splint functionassociated with multiple knots.These theorems possess specific form,that arc convenient forapplicaton;In the case of with simple knots or polynomial splint,the corollaries of this paper’s the-orems give corresponding results.

THE SARD BEST APPROXIMATION OF LINEAR FUNCTIONAL

In numerical analysis, it is significant to approximate the linear functional Ef=sum from i=0 to m-1([integral from a to b(a1（x）f1（x）dx+ sum from f=0 to i1(b1f1（x1）)]) by a simpler linear functional Lf=sum from i=1 to m（a1f（x1）） In this paper, making use of natural Tchebysheff spline function, we give existence theorem and uniqueness theorem of L that is exact for the degree m to F; we also give three sufficient and necessary conditions in which L is the Sard best approximation to F.

GLOBAL WEAK SHARP MINIMA AND COMPLETENESS OF METRIC SPACE

A sufficient condition on the existence of a global weak sharp minima for general function in metric space is established. A characterization for convex function to have global weak sharp minima is also presented, which generalized Burke and Ferris' result to infinite dimensional space. A characterization of the completeness of a metric space is given by the existence of global weak sharp minima.

COMPLETE CONVERGENCE FOR A CLASS OF MIXING SEQUENCES

Under some conditions on probability, the author obtains some results on the complete convergence for partial sums of not necessary identically distributed p-mixing se- quences, and the complete convergence for partial sums of B-valued martingale differences is also studied. As application the author gives the corresponding results on the complete convergence for randomly indexed partial sums.

K-THEORETICALLY COMPLETE VON NEUMANN REGULAR RINGS

The authors introduce the concept of Ko-complete ring and study the properties of Ko-complete unit-regular rings.

无创心肌做功评价完全性左束支传导阻滞患者左室功能的临床价值

目的 探讨无创心肌做功评价完全性左束支传导阻滞(CLBBB)患者左室功能的临床价值。方法 选取我院CLBBB患者56例,包括左室射血分数(LVEF)正常者30例(射血分数正常组)及LVEF减低者26例(射血分数减低组),另选同期年龄、性别与之匹配的40例健康志愿者作为对照组,应用常规超声心动图获取左室舒张末期容积(LVEDV)、左室收缩末期容积(LVESV)及LVEF;二维斑点追踪技术获取整体纵向峰值应变(GLS)、峰值应变离散度(PSD),结合纵向应变参数和血压获取心肌做功参数,包括整体做功效率(GWE)、整体做功指数(GWI)、整体有用功(GCW)、整体无用功(GWW)、18节段心肌做功指数(WI),比较各组上述参数的差异;分析心肌做功参数与LVEF、GLS、PSD的相关性。结果 与对照组比较,射血分数正常组和射血分数减低组GLS减低,PSD增加,射血分数减低组LVEDV、LVESV均增加,LVEF减低,差异均有统计学意义(均P<0.05);与射血分数正常组比较,射血分数减低组LVEDV、LVESV、PSD均增加,LVEF、GLS均减低,差异均有统计学意义(均P<0.05)。与对照组比较,射血分数正常组和射血分数减低组GWI、GWE均减低,GWW增加,射血分数减低组GCW减低,差异均有统计学意义(均P<0.05);与射血分数正常组比较,射血分数减低组GWI、GWE、GCW均减低,GWW增加,差异均有统计学意义(均P<0.05)。与对照组比较,射血分数正常组和射血分数减低组前间隔和后间隔基底段、中间段、心尖段WI均减低,射血分数正常组后壁、侧壁、前壁基底段及侧壁中间段WI均增加,下壁中间段、心尖段及后壁心尖段WI均减低,射血分数减低组前壁、下壁、后壁基底段、中间段、心尖段及侧壁中间段、心尖段WI均减低,差异均有统计学意义(均P<0.05);与射血分数正常组比较,射血分数减低组所有节段WI均减低,差异均有统计学意义(均P<0.05)。相关性分析显示,GWI、GWE、GCW与LVEF、GLS均呈正相关,与PSD均呈负相关(均P<0.001);GWW与LVEF、GLS均呈负相关,与PSD呈正相关(均P<0.001);侧壁、前间隔、后间隔基底段WI与LVEF、GLS均呈正相关,与PSD均呈负相关(均P<0.001)。结论 无创心肌做功在评价CLBBB患者左室整体及节段收缩功能方面有一定的临床应用价值。

再议量子理论的表述形式与诠释

量子力学建立至今已达百年,关于量子力学仍存留许多困惑与争议。我们注意到可能的原因是状态矢量表示理念的不一致,以及混淆了不同的波函数概率诠释。我们认识到,坚持把状态矢量表示为无量纲的对象,认清波函数的薛定谔、玻恩和狄拉克各自诠释的不同以及薛定谔、玻恩的概率诠释可以经由狄拉克完备性关系联系起来,认识到概率行为出现在无量纲的态矢/波函数与决定性的状态方程之外,则可以消除不少关于量子力学的误解。