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From Hölder Continuous Solutions of 3D Incompressible Navier-Stokes Equations to No-Finite time Blowup on [ 0,∞ ]

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Advances in Pure Mathematics 2024年第9期14卷 695-743页

作者： terry E. Moschandreou tVDSB London Ontario London Canada

this article gives a general model using specific periodic special functions, that is, degenerate elliptic Weierstrass P functions composed with the LambertW function, whose presence in the governing equations through the forcing terms simplify the periodic Navier Stokes equations (PNS) at the centers of arbitrary r balls of the 3-torus. the continuity equation is satisfied together with spatially periodic boundary conditions. the yicomponent forcing terms consist of a function F as part of its expression that is arbitrarily small in an r ball where it is associated with a singular forcing expression both for inviscid and viscous cases. As a result, a significant simplification occurs with a v3(vifor all velocity components) only governing PDE resulting. the extension of three restricted subspaces in each of the principal directions in the Cartesian plane is shown as the Cartesian product ℋ=Jx,t×Jy,t×Jz,t. On each of these subspaces vi,i=1,2,3is continuous and there exists a linear independent subspace associated with the argument of the W function. Here the 3-torus is built up from each compact segment of length 2R on each of the axes on the 3 principal directions x, y, and z. the form of the scaled velocities for non zero scaled δis related to the definition of the W function such that e−W(ξ)=W(ξ)ξwhere ξdepends on t and proportional to δ→0for infinite time t. the ratio Wξis equal to 1, making the limit δ→0finite and well defined. Considering r balls where the function F=(x−ai)2+(y−bi)2+(z−ci)2−ηset equal to −1e+rwhere r>0. is such that the forcing is singular at every distance r of centres of cubes each containing an r-ball. At the centre of the balls, the forcing is infinite. the main idea is that a system of singular initial value problems with infinite forcing is to be solved for where the velocities are shown to be locally Hölder continuous. It is proven that the limit of these singular problems shifts the finite time blowup time ti∗for first and higher deriv

关键词： Navier-Stokes Periodic Navier-Stokes Equations 3-torus Periodic Ball Sphere Hölder Continuous Functions Uniqueness Angular Velocity Velocity in terms of Vorticity

Existence of a Hölder Continuous Extension on Embedded Balls of the 3-torus for the Periodic Navier Stokes Equations

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Advances in Pure Mathematics 2024年第2期14卷 118-138页

作者： terry E. Moschandreou Intermediate Science and Mathematics TVDSB London Ontario Canada

this article gives a general model using specific periodic special functions, which is degenerate elliptic Weierstrass P functions whose presence in the governing equations through the forcing terms simplify the periodic Navier Stokes equations (PNS) at the centers of cells of the 3-torus. Satisfying a divergence-free vector field and periodic boundary conditions respectively with a general spatio-temporal forcing term which is smooth and spatially periodic, the existence of solutions which have finite time singularities can occur starting with the first derivative and higher with respect to time. the existence of a subspace of the solution space where v3 is continuous and {C, y1, y12}, is linearly independent in the additive argument of the solution in terms of the Lambert W function, (y12=y2, C∈R) together with the condition v2=-2y1v1. On this subspace, the Biot Savart Law holds exactly [see Section 2 (Equation (13))]. Also on this subspace, an expression X (part of PNS equations) vanishes which contains all the expressions in derivatives of v1 and v2 and the forcing terms in the plane which are related as with the cancellation of all such terms in governing PDE. the y3 component forcing term is arbitrarily small in ε ball where Weierstrass P functions touch the center of the ball both for inviscid and viscous cases. As a result, a significant simplification occurs with a v3 only governing PDE resulting. With viscosity present as v changes from zero to the fully viscous case at v =1 the solution for v3 reaches a peak in the third component y3. Consequently, there exists a dipole which is not centered at the center of the cell of the Lattice. Hence since the dipole by definition has an equal in magnitude positive and negative peak in y3, then the dipole Riemann cut-off surface is c

关键词： Navier-Stokes PNS 3-torus Periodic Ball Sphere Hölder Continuous Riemann-Surface Uniqueness

Recovery rates of persistent post-COVID-19 olfactory dysfunction using psychophysical assessment:A longitudinal cohort study

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World Journal of Otorhinolaryngology-Head and Neck Surgery 2024年第2期10卷 79-87页

作者： Jeremy P.tervo Patricia t.Jacobson Brandon J.Vilarello tiana M.Saak Francesco F.Caruana Liam W.Gallagher Joseph B.Gary David A.Gudis Paule V.Joseph D.P.Devanand terry E.Goldberg Jonathan B.Overdevest Columbia University Vagelos College of Physicians and Surgeons New YorkNew YorkUSA Department of Otolaryngology-Head and Neck Surgery New York-Presbyterian/Columbia University Irving Medical CenterNew YorkNew YorkUSA Department of Otolaryngology-Head and Neck Surgery University of PittsburghPittsburghPennsylvaniaUSA Department of Otolaryngology-Head and Neck Surgery University of MinnesotaMinneapolisMinnesotaUSA National Institute of Alcohol Abuse and Alcoholism Section of Sensory Science and Metabolism&National Institute of Nursing ResearchBethesdaMarylandUSA New york-Presbyterian/Columbia University Irving Medical Center New YorkNew YorkUSA

Objectives:Persistent olfactory dysfunction(OD)following loss of smell associated with SARS-CoV-2 infection is a major feature of long *** on the prevalence of persistent OD predominantly rely on self-reported olfactory *** studies have tracked longitudinal rates of recovery using psychophysical assessment among patients presenting for evaluation of persistent OD beyond a window of acute *** anchored in standardized testing methods are needed to counsel patients who fail to acutely regain their sense of *** study aims to quantify the degree of persistent OD in post-COVID-19 patients who experience subjective and psychophysical ***:We grouped participants presenting for OD evaluation into cohorts based on both subjective and psychophysical olfactory status at a baseline assessment and assessed their olfactory abilities with a visual analogue scale and the Sniffin'Sticks extended test at baseline and 1-year time *** had confirmed a history of COVID-19 by lab evaluation or clinical diagnosis if lab evaluation was not ***:Baseline olfactory evaluation was completed by 122 participants,53 of whom completed the 1-year follow-up *** participants presenting with perceived OD,74.5%had confirmed psychophysical OD at baseline,with 55.1%at 1-year *** had reliable trends in self-rated versus psychophysically tested olfactory function at both time *** total threshold,discrimination,and identification(tDI)score improved by+3.25 points in the cohort with psychophysical OD(p=0.0005),with this improvement largely attributable to an increase in median threshold scores(+2.75 points;p=0.0004).Conclusions:OD persists in a significant number of patients who fail to acutely recovery their sense of smell after COVID-19,with many demonstrating lingering deficits at *** in threshold,but not discrimination or identification,most significantly mediate improvement

关键词： long COVID olfaction post-COVID condition smell dysfunction

Exploring the epididymis： a personal perspective on ：areers in science

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Asian Journal of Andrology 2015年第5期17卷 704-707,I0005页

作者： terry t turner Department of Urology University of Virginia School of MedicineCharlottesvilleUSA

Science is a profession of inquiry. We ask ourselves what is it we see and why our observations happen the way they do. Answering those two question puts us in the company of those early explorers, who from Europe found the New World, and from Asia reached west to encounter Europe. Vasco Nunez de Balboa of Spain was such an explorer. He was the first European to see or ＂discover＂ the Pacific Ocean. One can imagine his amazement, his excitement when he first saw from a mountain top that vast ocean previously unknown to his culture. A career in science sends each of us seeking our own ＂Balboa Moments＂, those observations or results that surprise or even amaze us, those discoveries that open our eyes to new views of nature and medicine. Scientists aim to do what those early explorers did： discover what has previously been unknown, see what has previously been unseen, and reveal what has previously been hidden. Science requires the scientist to discover the facts from among many fictions and to separate the important facts from the trivial so that knowledge can be properly developed. It is only with knowledge that old dogmas can be challenged and corrected. Careers in science produce specific sets of knowledge. When pooled with other knowledge sets they eventually contribute to wisdom and it is wisdom, we hope, that will improve the human condition.

关键词：科学家就业附睾职业生涯资源管理器探险家欧洲西班牙

(Q)SAR modelling of nanomaterial toxicity:A critical review

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Particuology 2015年第4期13卷 1-19页

作者： Ceyda Oksel Cai y.Ma Jing J.Liu terry Wilkins Xue Z.Wang Institute of Particle Science and Engineering School of Chemical and Process EngineeringUniversity of Leeds School of Chemistry and Chemical Engineering South China University of Technology

there is increasing recognition that some nanomaterials may pose a risk to human health and the environment. Moreover, the industrial use of the novel engineered nanomaterials （ENMs） increases at a higher rate than data generation for hazard assessment; consequently, many of them remain untested. the large number of nanomaterials and their variants （e.g., different sizes and coatings） requiring testing and the ethical pressure towards nonanimal testing means that in a first instance, expensive animal bioassays are precluded, and the use of（quantitative） structure-activity relationships （（Q）SARs） models as an alter- native source of （screening） hazard information should be explored. （Q）SAR modelling can be applied to contribute towards filling important knowledge gaps by making best use of existing data, prioritizing the physicochemical parameters driving toxicity, and providing practical solutions for the risk assessment problems caused by the diversity of ENMs. this paper covers the core components required for successful application of （Q）SAR methods to ENM toxicity prediction, summarizes the published nano-（Q）SAR studies, and outlines the challenges ahead for nano-（Q）SAR modelling. It provides a critical review of （1） the present availability of ENM characterization/toxicity data, （2） the characterization of nanostructures that meet the requirements for （Q）SAR analysis, （3） published nano-（Q）SAR studies and their limitations, （4） in silico tools for （Q）SAR screening of nanotoxicity, and （5） prospective directions for the development of nano-（Q）SAR models.

关键词： Nanomaterial toxicity Nanotoxicology QSAR NanoSAR In silico toxicity prediction

yeast-generated CO2:A convenient source of carbon dioxide for mosquito trapping using the BG-Sentinel?traps

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Asian Pacific Journal of tropical Biomedicine 2017年第10期7卷 896-900页

作者： dhanique c.t.jerry terry mohammed azad mohammed University of the West Indies St AugustineTrinidad and Tobago

Objectives: to evaluates carbon dioxide(CO_2) production from yeast/sugar mixtures and its efficiency as an attractant in BG-Sentinel ***: the rate of CO_2 production was optimized for different yeast/sugar *** optimized mixture was then used as bait in BG-Sentinel traps. the efficiency of this bait was then compared to octenol baited ***: the yeast/sugar(5g: 280g) in 300 m L water generated the highest volume of CO_2. the CO_2 baited traps caught significantly more mosquitoes than octenol baited ***: yeast-produced CO_2 can effectively replace octenol baits in BG *** will significantly reduce costs and allow sustainable mass-application of the CO_2 baited traps in large scale surveillance programs.

关键词： trinidad and tobago Carbon dioxide bait BG sentinel trap Attractant

KMAP-O framework for care management research of patients with type 2 diabetes

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World Journal of Diabetes 2017年第4期8卷 165-171页

作者： thomas t H Wan Amanda terry Bobbie McKee Waleed Kattan College of Health and Public Affairs University of Central Florida Florida Hospital Creation Health Research Center

AIM to review impacts of interventions involving self-management education, health coaching, and motivational interviewing for type 2 diabetes. MEtHODS A thorough review of the scientific literature on diabetes care and management was executed by a research team. RESULtS this article summarizes important findings in regard to the validity of developing a comprehensive behavioral system as a framework for empirical investigation. the behavioral system framework consists of patients' knowledge(K), motivation(M), attitude(A), and practice(P) as predictor variables for diabetes care outcomes(O). Care management strategies or health education programs serve as the intervention variable that directly influences K, M, A, and P and then indirectly affects the variability in patient care outcomes of patients with type 2 diabetes. CONCLUSION this review contributes to the understanding of the KMAP-O framework and how it can guide the care management of patients with type 2 diabetes. It will allow the tailoring of interventions to be more effective through knowledge enhancement, increased motivation, attitudinal changes, and improved preventive practice to reduce the progression of type 2 diabetes and comorbidities. Furthermore, the use of health information technology for enhancing changes in KMAP and communications is advocated in health promotion and development.

关键词： KMAP-O framework type 2 diabetes Behavioral intervention strategies Causal mechanisms

Analysis of highway performance under mixed connected and regular vehicle environment

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Journal of Intelligent and Connected Vehicles 2021年第2期4卷 68-79页

作者： Zhao Zhang Xianfeng(terry)yang Department of Civil and Environmental Engineering University of UtahSalt Lake CityUSA

Purpose–this study aims to study the connected vehicle(CV)impact on highway operational performance under a mixed CV and regular vehicle(RV)***/methodology/approach–the authors implemented a mixed trafﬁcﬂow model,along with a CV speed control model,in the simulation *** to the different trafﬁc characteristics between CVs and RVs,this researchﬁrst analyzed how the operation of CVs can affect highway capacity under both one-lane and multi-lane cases.A hypothesis was then made that there shall exist a critical CV penetration rate that can signiﬁcantly show the beneﬁt of CV to the overall trafﬁ*** prove this concept,this study simulated the mixed trafﬁc pattern under various ***–the results of this research revealed that performing optimal speed control to CVs will concurrently beneﬁt RVs by improving highway ***,a critical CV penetration rate should exist at a speciﬁed trafﬁc demand level,which can signiﬁcantly reduce the speed difference between RVs and *** results offer effective insight to understand the potential impacts of different CV penetration rates on highway operation ***/value–this approach assumes that there shall exist a critical CV penetration rate that can maximize the beneﬁts of CV *** penetration rate(the proportion of CVs in mixed trafﬁc)is the key factor affecting the impacts of CV on freeway operational *** evaluation criteria for freeway operational performance are using average travel time under different given trafﬁc demand patterns.

关键词： Connected vehicle Highway capacity Mixed trafﬁc Penetration rate Variable speed limit Paper type Research

Segment boundaries of the adult rat epididymis limit interstitial signaling by potential paracrine factors and segments lose differential gene expression after efferent duct ligation

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Asian Journal of Andrology 2007年第4期9卷 565-573页

作者： terry t. tumer Daniel S. Johnston Scott A. Jelinsky Jose L. tomsig Joshua N. Finger Department of Urology University of Virginia Health Science System Charlottesville VA 22908 US Cell Biology University of Virginia Health Science System Charlottesville VA 22908 US Contraception Women＇s Health and Musculoskeletal Biology Wyeth Research Collegeville PA 19426 USA Biological technologies Molecular Profiling and Biomarker Discovery Wyeth Research Cambridge MA 02140 USA

the epididymis is divided into caput, corpus and cauda regions, organized into intraregional segments separated by connective tissue septa （CtS）. In the adult rat and mouse these segments are highly differentiated. Regulation of these segments is by endocrine, lumicrine and paracrine factors, the relative importance of which remains under investigation. Here, the ability of the CtS to limit signaling in the interstitial compartment is reviewed as is the effect of 15 days of unilateral efferent duct ligation （EDL） on ipsilateral segmental transcriptional profiles. Inter-segmental microperifusions of epidermal growth factor （EGF）, vascular endothelial growth factor （VEGFA） and fibroblast growth factor 2 （FGF2） increased phosphorylation of mitogen activated protein kinase （MAPK） in segments 1 and 2 of the rat epididymis and the effects of all factors were limited by the CtS separating the segments. Microan＇ay analysis of segmental gene expression determined the effect of 15 days of unilateral EDL on the transcriptome-wide gene expression of rat segments 1-4. Over 11 000 genes were expressed in each of the four segments and over 2 000 transcripts in segment 1 responded to deprivation of testicular lumicrine factors. Segments 1 and 2 of control tissues were the most transcriptionally different and EDL had its greatest effects there. In the absence of lumicrine factors, all four segments regressed to a transcriptionally undifferentiated state, consistent with the less differentiated histology. Deprivation of lumicrine factors could stimulate an individual gene＇s expression in some segments yet suppress it in others. Such results reveal a higher complexity of the regulation of rat epididymal segments than that is generally appreciated. （Asian J Androl 2007 July; 9： 565-573）

关键词： efferent duct ligation dedifferentiation proximal epididymis