The Products of Regularly Solvable Operators with Their Spectra in Direct Sum Spaces

In this paper, we consider the general quasi-differential expressions each of order n with complex coefficients and their formal adjoints on the interval (a,b). It is shown in direct sum spaces of functions defined on each of the separate intervals with the cases of one and two singular end-points and when all solutions of the equation and its adjoint are in (the limit circle case) that all well-posed extensions of the minimal operator have resolvents which are HilbertSchmidt integral operators and consequently have a wholly discrete spectrum. This implies that all the regularly solvable operators have all the standard essential spectra to be empty. These results extend those of formally symmetric expression studied in [1-10] and those of general quasi-differential expressions in [11-19].

Clustered Regularly Interspaced Short Palindromic Repeats(CRISPR):A critical overview on the most promising applications of molecular scissors in oral medicine

The scientific community is continuously working to translate the novel biomedical techniques into effective medical treatments.CRISPR-Cas9 system(Clustered Regularly Interspaced Short Palindromic Repeats-9),commonly known as the“molecular scissor”,represents a recently developed biotechnology able to improve the quality and the efficacy of traditional treatments,related to several human diseases,such as chronic diseases,neurodegenerative pathologies and,interestingly,oral diseases.Of course,dental medicine has notably increased the use of biotechnologies to ensure modern and conservative approaches:in this landscape,the use of CRISPR-Cas9 system may speed and personalize the traditional therapies,ensuring a good predictability of clinical results.The aim of this critical overview is to provide evidence on CRISPR efficacy,taking into specific account its applications in oral medicine.

Relationship among intermittent pulse,regularly intermittent pulse,and bradyarrhythmia

Pulse diagnosis is an important basis for the diagnosis of Chinese medicine.It is the rich experience accumulated by the predecessors in the long and continuous practice,and it is a unique diagnosis method of Chinese medicine.There are many names of pulse conditions in traditional Chinese medicine.The four elements are analyzed and summarized in terms of position,number,shape,and momentum.The four elements are used as 28 kinds of pulses.Among them,the regularly intermittent pulse and the intermittent pulse are characterized by arrhythmia and intermittent stop of the pulse.Intermittent pulse means irregular intervals;when a pulse comes,Regularly Intermittent pulse have regular stops.This kind of phenomenon is similar to the bradyarrhythmia in modern medicine.The knot pulse is an irregular pulse stopping,which can be seen clinically in sinus arrest,second-degree type I sinus block,second-degree type I atrioventricular block,and escape beats and so on.On the other hand,Regularly Intermittent pulse is a regular pulse stopping,which can be clinically found in the second degree type II sinus block,the second degree type II sinus block,and the second degree type I atrioventricular block with a special 2:1 type of atrioventricular block type and so on.

THE SMOOTHING EFFECT IN SHARP GEVREY SPACE FOR THE SPATIALLY HOMOGENEOUS NON-CUTOFF BOLTZMANN EQUATIONS WITH A HARDPOTENTIAL

In this article, we study the smoothing effect of the Cauchy problem for the spatially homogeneous non-cutoff Boltzmann equation for hard potentials. It has long been suspected that the non-cutoff Boltzmann equation enjoys similar regularity properties as to whose of the fractional heat equation. We prove that any solution with mild regularity will become smooth in Gevrey class at positive time, with a sharp Gevrey index, depending on the angular singularity. Our proof relies on the elementary L^(2) weighted estimates.

Distributed Optimal Formation Control for Unmanned Surface Vessels by a Regularized Game-Based Approach

Dear Editor,This letter explores optimal formation control for a network of unmanned surface vessels(USVs).By designing an individual objective function for each USV,the optimal formation problem is transformed into a noncooperative game.Under this game theoretic framework,the optimal formation is achieved by seeking the Nash equilibrium of the regularized game.A modular structure consisting of a distributed Nash equilibrium seeker and a regulator is proposed.

SHARP MORREY REGULARITY THEORY FOR A FOURTH ORDER GEOMETRICAL EQUATION

This paper is a continuation of recent work by Guo-Xiang-Zheng[10].We deduce the sharp Morrey regularity theory for weak solutions to the fourth order nonhomogeneous Lamm-Rivière equation △^{2}u=△(V▽u)+div(w▽u)+(▽ω+F)·▽u+f in B^(4),under the smallest regularity assumptions of V,ω,ω,F,where f belongs to some Morrey spaces.This work was motivated by many geometrical problems such as the flow of biharmonic mappings.Our results deepens the Lp type regularity theory of[10],and generalizes the work of Du,Kang and Wang[4]on a second order problem to our fourth order problems.

Enhanced Differentiable Architecture Search Based on Asymptotic Regularization

In differentiable search architecture search methods,a more efficient search space design can significantly improve the performance of the searched architecture,thus requiring people to carefully define the search space with different complexity according to various operations.Meanwhile rationalizing the search strategies to explore the well-defined search space will further improve the speed and efficiency of architecture search.With this in mind,we propose a faster and more efficient differentiable architecture search method,AllegroNAS.Firstly,we introduce a more efficient search space enriched by the introduction of two redefined convolution modules.Secondly,we utilize a more efficient architectural parameter regularization method,mitigating the overfitting problem during the search process and reducing the error brought about by gradient approximation.Meanwhile,we introduce a natural exponential cosine annealing method to make the learning rate of the neural network training process more suitable for the search procedure.Moreover,group convolution and data augmentation are employed to reduce the computational cost.Finally,through extensive experiments on several public datasets,we demonstrate that our method can more swiftly search for better-performing neural network architectures in a more efficient search space,thus validating the effectiveness of our approach.

贝索夫空间中三维布辛涅斯克方程的一些新的正则性准则

In this paper, we study the regularity criterion for the three-dimensional Boussinesq equations in Besov spaces. We show that the smooth solution(u,θ) is regular if the horizonal velocity u_h holds ■.

Composition Analysis and Identification of Ancient Glass Products Based on L1 Regularization Logistic Regression

In view of the composition analysis and identification of ancient glass products, L1 regularization, K-Means cluster analysis, elbow rule and other methods were comprehensively used to build logical regression, cluster analysis, hyper-parameter test and other models, and SPSS, Python and other tools were used to obtain the classification rules of glass products under different fluxes, sub classification under different chemical compositions, hyper-parameter K value test and rationality analysis. Research can provide theoretical support for the protection and restoration of ancient glass relics.

Low-Rank Multi-View Subspace Clustering Based on Sparse Regularization

Multi-view Subspace Clustering (MVSC) emerges as an advanced clustering method, designed to integrate diverse views to uncover a common subspace, enhancing the accuracy and robustness of clustering results. The significance of low-rank prior in MVSC is emphasized, highlighting its role in capturing the global data structure across views for improved performance. However, it faces challenges with outlier sensitivity due to its reliance on the Frobenius norm for error measurement. Addressing this, our paper proposes a Low-Rank Multi-view Subspace Clustering Based on Sparse Regularization (LMVSC- Sparse) approach. Sparse regularization helps in selecting the most relevant features or views for clustering while ignoring irrelevant or noisy ones. This leads to a more efficient and effective representation of the data, improving the clustering accuracy and robustness, especially in the presence of outliers or noisy data. By incorporating sparse regularization, LMVSC-Sparse can effectively handle outlier sensitivity, which is a common challenge in traditional MVSC methods relying solely on low-rank priors. Then Alternating Direction Method of Multipliers (ADMM) algorithm is employed to solve the proposed optimization problems. Our comprehensive experiments demonstrate the efficiency and effectiveness of LMVSC-Sparse, offering a robust alternative to traditional MVSC methods.

A New Result on Regular Designs under Baseline Parameterization

The study on designs for the baseline parameterization has aroused attention in recent years. This paper focuses on two-level regular designs for the baseline parameterization. A general result on the relationship between K-aberration and word length pattern is developed.

Decentralized Semi-Supervised Learning for Stochastic Configuration Networks Based on the Mean Teacher Method

The aim of this paper is to broaden the application of Stochastic Configuration Network (SCN) in the semi-supervised domain by utilizing common unlabeled data in daily life. It can enhance the classification accuracy of decentralized SCN algorithms while effectively protecting user privacy. To this end, we propose a decentralized semi-supervised learning algorithm for SCN, called DMT-SCN, which introduces teacher and student models by combining the idea of consistency regularization to improve the response speed of model iterations. In order to reduce the possible negative impact of unsupervised data on the model, we purposely change the way of adding noise to the unlabeled data. Simulation results show that the algorithm can effectively utilize unlabeled data to improve the classification accuracy of SCN training and is robust under different ground simulation environments.

On the Cauchy Problem for Mildly Nonlinear and Non-Boussinesq Case-(ABC) System

In this paper, we investigate the local well-posedness, ill-posedness, and Gevrey regularity of the Cauchy problem for Mildly Nonlinear and Non-Boussinesq case-(ABC) system. The local well-posedness of the solution for this system in Besov spaces B p,r s 1 × B p,r s with 1≤p,r≤∞ and s>max{ 1 1 p , 3 2 } was firstly established. Next, we consider the continuity of the solution-to-data map, i.e. the ill-posedness of the solution for this system in Besov space B p,∞ s 1 × B p,∞ s was derived. Finally, the Gevrey regularity of the system was presented.

The Regularity of Solutions to Mixed Boundary Value Problems of Second-Order Elliptic Equations with Small Angles

This paper considers the regularity of solutions to mixed boundary value problems in small-angle regions for elliptic equations. By constructing a specific barrier function, we proved that under the assumption of sufficient regularity of boundary conditions and coefficients, as long as the angle is sufficiently small, the regularity of the solution to the mixed boundary value problem of the second-order elliptic equation can reach any order.

Tail Distortion Risk Measure for Portfolio with Multivariate Regularly Variation

For the multiplicative background risk model,a distortion-type risk measure is used to measure the tail risk of the portfolio under a scenario probability measure with multivariate regular variation.In this paper,we investigate the tail asymptotics of the portfolio loss ∑_(i=1)^(d)R_(i)S,where the stand-alone risk vector R=(R_(1),...,R_(d))follows a multivariate regular variation and is independent of the background risk factor S.An explicit asymptotic formula is established for the tail distortion risk measure,and an example is given to illustrate our obtained results.

益生菌遗传育种方法研究进展

益生菌的多样化益生作用使其在人类健康领域发挥着重要作用,基于益生菌生产的药品、食品和膳食补充剂也受到越来越多的关注。目前,研究人员致力于为药品和食品行业选育新型益生菌,以期为食品药品行业的发展提供新的思路。遗传育种为选育具有有益特性的益生菌菌株提供了一个很好的平台,这对提升益生菌的市场价值和人类健康具有重要意义。为了今后更好的开展益生菌育种工作,该文综述了原生质体融合、基因组重排、常压室温等离子体诱变及基因编辑技术[成簇规律间隔的短回文重复序列相关蛋白(clustered regularly interspaced short palindromic repeats-associated,CRISPR-Cas)技术和碱基编辑技术]等遗传育种技术的研究现状及在益生菌中的应用,并讨论了遗传育种的安全性,旨在为优良益生菌的选育提供参考,促进益生菌资源的开发和利用。

Neurologic orphan diseases:Emerging innovations and role for genetic treatments

Orphan diseases are rare diseases that affect less than 200000 individuals within the United States.Most orphan diseases are of neurologic and genetic origin.With the current advances in technology,more funding has been devoted to developing therapeutic agents for patients with these conditions.In our review,we highlight emerging options for patients with neurologic orphan diseases,specifically including diseases resulting in muscular deterioration,epilepsy,seizures,neurodegenerative movement disorders,inhibited cognitive development,neuron deterioration,and tumors.After extensive literature review,gene therapy offers a promising route for the treatment of neurologic orphan diseases.The use of clustered regularly interspaced palindromic repeats/Cas9 has demonstrated positive results in experiments investigating its role in several diseases.Additionally,the use of adeno-associated viral vectors has shown improvement in survival,motor function,and developmental milestones,while also demonstrating reversal of sensory ataxia and cardiomyopathy in Friedreich ataxia patients.Antisense oligonucleotides have also been used in some neurologic orphan diseases with positive outcomes.Mammalian target of rapamycin inhibitors are currently being investigated and have reduced abnormal cell growth,proliferation,and angiogenesis.Emerging innovations and the role of genetic treatments open a new window of opportunity for the treatment of neurologic orphan diseases.

Targeting KRAS in pancreatic adenocarcinoma:Progress in demystifying the holy grail

Pancreatic cancer(PC)remains one of the most challenging diseases,with a very poor 5-year overall survival of around 11.5%.Kirsten rat sarcoma virus(KRAS)mutation is seen in 90%-95%of PC patients and plays an important role in cancer cell proliferation,differentiation,metabolism,and survival,making it an essential mutation for targeted therapy.Despite extensive efforts in studying this oncogene,there has been little success in finding a drug to target this pathway,labelling it for decades as“undruggable”.In this article we summarize some of the efforts made to target the KRAS pathway in PC,discuss the challenges,and shed light on promising clinical trials.

The Well-Posed Operators with Their Spectra in Lpw-Spaces

In this paper, we have considered the general ordinary quasi-differential operators generated by a general quasi-differential expression τp,q in Lpw-spaces of order n with complex coefficients and its formal adjoint τ+q',p' in Lpw-spaces for arbitrary p,q∈[1,∞). We have proved in the case of one singular end-point that all well-posed extensions of the minimal operator T0 (τp,q) generated by such expression τp,q and their formal adjoint on the interval [a,b) with maximal deficiency indices have resolvents which are Hilbert-Schmidt integral operators and consequently have a wholly discrete spectrum. This implies that all the regularly solvable operators have all the standard essential spectra to be empty. Also, a number of results concerning the location of the point spectra and regularity fields of the operators generated by such expressions can be obtained. Some of these results are extensions or generalizations of those in the symmetric case, while others are new.

Comparison of the interface reaction behaviors of CaO–V_(2)O_(5) and MnO_(2)–V_(2)O_(5) solid-state systems based on the diffusion couple method

The formation mechanism of calcium vanadate and manganese vanadate and the difference between calcium and manganese in the reaction with vanadium are basic issues in the calcification roasting and manganese roasting process with vanadium slag.In this work,CaO–V_(2)O_(5) and MnO_(2)–V_(2)O_(5) diffusion couples were prepared and roasted for different time periods to illustrate and compare the diffusion reaction mechanisms.Then,the changes in the diffusion product and diffusion coefficient were investigated and calculated based on scanning electron microscopy (SEM) with energy dispersive X-ray spectroscopy (EDS) analysis.Results show that with the extension of the roasting time,the diffusion reaction gradually proceeds among the CaO–V_(2)O_(5) and MnO_(2)–V_(2)O_(5) diffusion couples.The regional boundaries of calcium and vanadium are easily identifiable for the CaO–V_(2)O_(5) diffusion couple.Meanwhile,for the MnO_(2)–V_(2)O_(5) diffusion couple,MnO_(2) gradually decomposes to form Mn_(2)O_(3),and vanadium diffuses into the interior of Mn_(2)O_(3).Only a part of vanadium combines with manganese to form the diffusion production layer.CaV_(2)O_(6) and MnV_(2)O_(6) are the interfacial reaction products of the CaO–V_(2)O_(5) and MnO_(2)–V_(2)O_(5) diffusion couples,respectively,whose thicknesses are 39.85 and 32.13μm when roasted for 16 h.After 16 h,both diffusion couples reach the reaction equilibrium due to the limitation of diffusion.The diffusion coefficient of the CaO–V_(2)O_(5) diffusion couple is higher than that of the MnO_(2)–V_(2)O_(5) diffusion couple for the same roasting time,and the diffusion reaction between vanadium and calcium is easier than that between vanadium and manganese.