On capped Higgs positivity cone

The Wilson coefficients of the standard model effective field theory are subject to a series of positivity bounds.It has been shown that while the positivity part of the ultraviolet(UV)partial wave unitarity leads to the Wilson coefficients living in a convex cone,further including the nonpositivity part caps the cone from above.For Higgs scattering,a capped positivity cone was obtained using a simplified,linear unitarity condition without utilizing the full internal symmetries of Higgs scattering.Here,we further implement stronger nonlinear unitarity conditions from the UV,which generically gives rise to better bounds.We show that,for the Higgs case in particular,while the nonlinear unitarity conditions per se do not enhance the bounds,the fuller use of the internal symmetries do shrink the capped positivity cone significantly.

The Expression of Apoptosis-Related Genes Bcl-2 and Bax Protein and Apoptosis Positivity in Cervical Carcinoma during Irradiation

To evaluate the apoptosis positivity, the expression of Bcl-2, bax proteinsin 30 patients with squamous cell cervix carcinoma before and after radiotherapy. Methods: By usingimmuno-histochemical and TDT-dUTP nick end labelling techniques, 30 cases of squamous cell cervicalcarcinoma were analyzed. Results: The apoptosis positivity before and after irradiation was 76.7%and 100% respectively, with the difference being significant (P 【 0.05); The positive rates of Bcl-2protein before and after irradiation were 73.3% and 46.7% respectively, with the difference beingsignificant (P 【 0.05); The positive rates of bax protein before and after irradiation were 86% and100% respectively, with the difference being significant (P 【 0.05). Conclusion: bax and Bcl-2protein play an important role in apoptosis induced by fractionated radiation therapy. Apoptosisinduced by irradiation is contributed to upregulation of bax protein or downregulation of Bcl-2protein.

HIGH RESOLUTION POSITIVITY-PRESERVING DIFFERENCE SCHEMES FOR TWO DIMENSIONAL EULER EQUATIONS

A class of high resolution positivity preserving Boltzmann type difference schemes for one and two dimensional Euler equations is studied. First, the relation between Boltzmann and Euler equations is analyzed. By using a kind of special interpolation, the high resolution Boltzmann type difference scheme is constructed. Finally, numerical tests show that the schemes are effective and useful.

Convexity and Positivity of Bivariate Quadratic Bézier Surfaces over a Rectangle

With the help of several discriminants about the zero points of a quartic polynomial, the sufficient and necessary conditions for the positivity and nonnegativity of the quartic polynomial over an interval I(-∞,+∞) was derived. Based on these conclusions, the sufficient and necessary conditions for the positivity and convexity of the 2×2 Bézier surface over a rectangle were obtained. A simple sufficient condition was deduced also and finally several examples were given.

Determinants of Persistent Sputum Smear Positivity after Intensive Phase Chemotherapy among Patients with Tuberculosis at Rhodes Chest Clinic, Nairobi, Kenya

The prevalence of TB in sub-Sahara Africa has been reported as 511 per 100,000 populations and a mortality of 74 per 100,000 in year 2009. In the same period, incidence was estimated at 350 cases per 100,000. In this regard, the health system requires strengthening to respond to the rising cases of infection, drug resistance and quality of life lost while continuing to seek interventions that improve adherence to medication and case detection among those infected. Methods: This study sought to determine factors that are associated with sputum positivity after intensive phase of chemotherapy in people with tuberculosis. It was a retrospective case-control study conducted in Rhodes chest clinic, a City Council health unit in Nairobi that specializes in treatment of chest infections. The participants were sampled from clinic attendants who had completed two months of intensive phase TB chemotherapy and met inclusion criteria. Results: Seventy participants of whom 25 (36%) were sputum positive at the end of two (2) months intensive phase were included in the study. Skipping medication doses was significantly associated with sputum positivity (p = 0.01). Patients who were sputum positive at the end of the two-month period were more likely to have taken longer time before seeking treatment compared to those who were sputum negative by median (IQR) 8 (3 - 12) and 4 (3 - 8) weeks respectively although this difference was not significant (p = 0.09). Patients who had not disclosed their infection status had a two-fold possibility of remaining sputum positive at the end of intensive phase. Conclusion: Early diagnosis and treatment of TB, and adherence to medication were important factors that affect sputum conversion during intensive phase of TB treatment. Therefore, public health practitioners should advise patients to seek prompt diagnosis and treatment of signs and symptoms of tuberculosis.

Complete Positivity of Elementary Operators on C^＊—algebras

Let E(x) = be an elementary operator on a C-algebra A. We prove that if A is prime with soc(A) = 0, or there is a family of irreducible representation of A such that is faithful and (A) does not contain compact operator,or A has a faithful repre sentation π such that π(A)″with no central portions of type In for n>1 then E is positive if and only if E is completely positive.

The Role of Photographs and Time Lag on Positivity Ratings of Vaca­tion and Weekend Memories

Two studies examined the question of whether photograph taking of an event influences the positivity of the evaluations of the event at a later point in time.Memories of photographed events yielded higher positivity ratings than memories that were not photographed.Although we expected fading of positivity ratings to occur more slowly over a period of two months for memories of photographed events,we found faster affect fading for those memories in Study 2 instead.The findings of the two studies support the idea that taking photographs of events sustains the affective reconstruction of autobiographical memories,regardless of whether these events are special,such as vacation memories,or more mundane,such as memories of the past weekend.

Total Positivity of UE Spline Basis

A new geometric method to prove the total positivity of UE spline basis was proposed. UE spline basis is a kind of basis defined over algebraic-trigonometric unified space. UE spline basis shares most properties of the usual polynomial B-Splines. Total positivity is an important property for spline basis, it is highly related with shape preserving and variation diminishing properties. Knot inserted algorithm is the most useful algorithm for spline curves since many other useful properties are based on it. It is necessary to prove the total positivity of UE spline basis using knot inserted algorithm intuitively, not only enrich the UE spline basis theory, but also can be treated as supplement to the total positivity in algebraic sense. This approach also can be extended to other analogical bases.

Positivity-Preserving Numerical Methods for Belousov-Zhabotinsky Reaction

The existence of positive solutions to the system of ordinary differential equations related to the Belousov-Zhabotinsky reaction is established. The key idea is to use a new successive approximation of solutions, ensuring its positivity. To obtain the positivity and invariant region for numerical solutions, the system is discretized as difference equations of explicit form, employing operator splitting methods with linear stability conditions. Algorithm to solve the alternate solution is given.

hh-transforms of Positivity Preserving Semigroups and Associated Markov Processes

The hh-transforms of positivity preserving semigroups and their associated Markov processes are investigated in this paper. In particular, it is shown that any quasi-regular positivity preserving coercive form is hh-associated with a pair of special standard processes which are in weak duality.

Extinction and Positivity for a Doubly Nonlinear Degenerate Parabolic Equation

The aims of this paper are to discuss the extinction and positivity for the solution of the initial boundary value problem and Cauchy problem of ut = div（[↓△u^m｜p-2↓△u^m）. It is proved that the weak solution will be extinct for 1 〈 p ≤ 1 ＋ 1/m and will be positive for p 〉 1 ＋ 1/m for large t, where m 〉 0.

Positivity and Stability of Fractional-Order Linear Time-Delay Systems

This article focuses on the positivity and the asymptotic stability of fractional-order linear time-delay systems(FOLTDSs)which are composed of N(N≥2)subsystems.Firstly,a sufficient and necessary condition is given to ensure the positivity of FOLTDSs.The solutions of the studied systems are obtained by using the Laplace transform method,and it can be observed that the positivity of FOLTDSs is completely determined by the series of matrices and independent of the magnitude of time-delays.Secondly,a theorem is given to prove the asymptotic stability of positive FOLTDSs.By considering the monotonicity and asymptotic properties of systems with constant time-delay,it is further shown that the asymptotic stability of positive FOLTDSs is independent of the time-delay.Next,a state-feedback controller,whose gain matrix is derived by resolving a linear programming question,is designed such that the state variables of the systems are nonnegative and asymptotically convergent.When the order of the FOLTDSs is greater than one,by utilizing a proposed property of Caputo derivative,a sufficient condition for the positivity of FOLTDS is presented.Finally,simulation examples are presented to verify the validity and practicability of the theoretical analysis.

Positivity and boundedness preserving schemes for the fractional reaction-difusion equation

In this paper, we design a semi-implicit scheme for the scalar time fractional reaction-diffusion equation. We theoretically prove that the numerical scheme is stable without the restriction on the ratio of the time and space stepsizes, and numerically show that the convergence orders are 1 in time and 2 in space. As a concrete model, the subdiffusive predator-prey system is discussed in detail. First, we prove that the analytical solution to the system is positive and bounded. Then, we use the provided numerical scheme to solve the subdiffusive predator-prey system, and theoretically prove and numerically verify that the numerical scheme preserves the positivity and boundedness.

Eventual Positivity of Hermitian Polynomials and Integral Operators

Quillen proved that if a Hermitian bihomogeneous polynomial is strictly positive on the unit sphere, then repeated multiplication of the standard sesquilinear form to this polynomial eventually results in a sum of Hermitian squares. Catlin-D'Angelo and Varolin deduced this positivstellensatz of Quillen from the eventual positive-definiteness of an associated integral operator. Their arguments involve asymptotic expansions of the Bergman kernel. The goal of this article is to give an elementary proof of the positive-definiteness of this integral operator.

A well-balanced positivity preserving two-dimensional shallow flow model with wetting and drying fronts over irregular topography

This paper presents an improved well-balanced Godunov-type 2-D finite volume model with structured grids to simulate shallow flows with wetting and drying fronts over an irregular topography. The intercell flux is computed using a central upwind scheme, which is a Riemann-problem-solver-free method for hyperbolic conservation laws. The nonnegative reconstruction method for the water depth is implemented to resolve the stationary or wet/dry fronts. The bed slope source term is discretized using a central difference method to capture the static flow state over the irregular topography. Second-order accuracy in space is achieved by using the slope limited linear reconstruction method. With the proposed method, the model can avoid the partially wetting/drying cell problem and maintain the mass conservation. The proposed model is tested and verified against three theoretical benchmark tests and two experimental dam break flows. Further, the model is applied to predict the maximum water level and the flood arrival time at different gauge points for the Malpasset dam break event. The predictions agree well with the numerical results and the measurement data published in literature, which demonstrates that with the present model, a well-balanced state can be achieved and the water depth can be nonnegative when the Courant number is kept less than 0.25.

Patients with Prolonged Positivity of SARS-CoV-2 RNA Benefit from Convalescent Plasma Therapy:A Retrospective Study

Convalescent plasma therapy has been implemented in a few cases of severe coronavirus disease 2019.No report about convalescent plasma therapy in treating patients with prolonged positivity of SARS-CoV-2 RNA has been published.In this study,we conducted a retrospective observational study in 27 patients with prolonged positivity of SARS-CoV-2 RNA,the clinical benefit of convalescent plasma therapy were analyzed.q RT-PCR test of SARS-CoV-2 RNA turned negative(B 7 days)in a part of patients(early negative group,n=15)after therapy,others(late negative group,n=12)turned negative in more than 7 days.Pulmonary imaging improvement was confirmed in 7 patients in early negative group and 8 in late negative group after CP therapy.Viral load decreased in early negative group compared with late negative group at day 3,5,7 after implementing convalescent plasma therapy.Patients in early negative group had a shorter median length of hospital stay.In conclusion,convalescent plasma therapy might help eliminate virus and shorten length of hospital stay in patients with prolonged positivity of SARS-CoV-2 RNA.

Positivity in electron-positron scattering:testing the axiomatic quantum field theory principles and probing the existence of UV states

We consider the positivity bounds on dimension-8 four-electron operators and study two related phenomenological aspects at future lepton colliders.First,if positivity is violated,probing such violations will revolutionize our understanding of the fundamental pillars of quantum field theory and the S-matrix theory.We observe that positivity violation at scales of 1-10 TeV can potentially be probed at future lepton colliders even if one assumes that dimension-6 operators are also present.Second,the positive nature of the dimension-8 parameter space often allows us to either directly infer the existence of UV-scale particles together with their quantum numbers or exclude them up to certain scales in a model-independent way.In particular,dimension-8 positivity plays an important role in the test of the Standard Model.If no deviations from the Standard Model are observed,it allows for simultaneous exclusion limits on all kinds of potential UV-complete models.Unlike the dimension-6 case,these limits apply regardless of the UV model setup and cannot be removed by possible cancellations among various UV contributions.This thus consists of a novel and universal test to confirm the Standard Model.We demonstrate with realistic examples how all the previously mentioned possibilities,including the test of positivity violation,can be achieved.Hence,we provide an important motivation for studying dimension-8 operators more comprehensively.

Advancements and challenges in neuroimaging for the diagnosis of intracranial aneurysms:Addressing false positive diagnoses and emerging techniques

Despite advancements in neuroimaging,false positive diagnoses of intracranial aneurysms remain a significant concern.This article examines the causes,prevalence,and implications of such false-positive diagnoses.We discuss how conditions like arterial occlusion with vascular stump formation and infundibular widening can mimic aneurysms,particularly in the anterior circulation.The article compares various imaging modalities,including computer tomography angiogram,magnetic resonance imaging/angiography,and digital subtraction angiogram,highlighting their strengths and limitations.We emphasize the im-portance of accurate differentiation to avoid unnecessary surgical interventions.The potential of emerging technologies,such as high-resolution vessel wall ima-ging and deep neural networks for automated detection,is explored as promising avenues for improving diagnostic accuracy.This manuscript underscores the need for continued research and clinical vigilance in the diagnosis of intracranial aneurysms.

Correlation analyse between thyroid hormone levels and severity of schizophrenia symptoms

BACKGROUND The imbalance of hormone levels in the body is closely related to the occurrence and progression of schizophrenia,especially thyroid hormones.AIM To study the relationship between triiodothyronine(T3),thyroxine(T4),free T3(FT3),free T4(FT4),thyroid stimulating hormone(TSH)and schizophrenia.METHODS In this study,100 schizophrenia patients were selected from our hospital between April 2022 and April 2024.Their clinical data were analyzed retrospectively.Based on the Positive and Negative Syndrome Scale(PANSS)score,patients were divided into mild(1-3 points,n=39),moderate(4 points,n=45),and severe groups(5-7 points,n=16).Additionally,55 healthy individuals served as a control group.Venous blood samples were collected to measure T3,T4,FT3,FT4,TSH,and cortisol concentrations,analyzing their relationship with PANSS scores.RESULTS The serum levels of T3,FT3,FT4,TSH and cortisol in the schizophrenia group were lower than those in the control group(P<0.05).With the increase of the severity of the disease,the concentrations of T3 and T4 decreased,while the con-centrations of TSH and cortisol increased(P<0.05).The concentrations of TSH and cortisol were positively correlated with the PANSS score,while T3 and T4 were negatively correlated with the PANSS score(P<0.05).The receiver ope-rating characteristic curve results showed that T3,T4,TSH,and cortisol had good efficacy in the diagnosis of schizophrenia.Logistic results showed that decreased T3 level,decreased T4 level,decreased TSH level and increased cortisol level may be independent risk factors for schizophrenia.CONCLUSION Thyroid hormone levels are associated with the severity of schizophrenia symptoms,which can provide new solutions for the diagnosis and treatment of schizophrenia.

THE STRICT POSITIVITY IN A NONSTANDARD HULL AND ITS APPLICATIONS TO ECONOMICS

The purpose of this paper is to study the strict positivity in a nonstandard hull of an internal normed Riesz space. Several characterizations are obtained for an element of the hull to be strictly positive. Particularly, it is shown that a nonstandard hull of an internal normed Riesz space has strictly positive elements if and only if it has an order unit. This result has an application to the double infillity problem in economics. It follows that the existence of equilibria in a nonstandard double infinity economy is equivalent to the existence of finite equilibria.