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Where Is Phase Velocity in Minkowski Space?

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j.urnal of Modern Physics 2024年第10期15卷 1555-1566页

作者： Antony j. Bourdillon Ultra-High Resolution Lithography San Jose CA USA

In the special theory of relativity, massive particles can travel at neither the speed of light c nor faster. Meanwhile, since the photon was quantized, many have thought of it as a point particle. How pointed? The idea could be a mathematical device or physical simplification. By contrast, the preceding notion of wave-group duality has two velocities: a group velocity vg and a phase velocity vp. In light vp = vg = c;but it follows from special relativity that, in massive particles, vp > c. The phase velocity is the product of the two best measured variables, and so their product constitutes internal motion that travels, verifiably, faster than light. How does vp then appear in Minkowski space? For light, the spatio-temporal Lorentz invariant metric is s2=c2t2−x2−y2−z2, the same in whatever frame it is viewed. The space is divided into 3 parts: firstly a cone, symmetric about the vertical axis ct > 0 that represents the world line of a stationary particle while the conical surface at s = 0 represents the locus for light rays that travel at the speed of light c. Since no real thing travels faster than the speed of light c, the surface is also a horizon for what can be seen by an observer starting from the origin at time t = 0. Secondly, an inverted cone represents, equivalently, time past. Thirdly, outside the cones, inaccessible space. The phase velocity vp, group velocity vg and speed of light are all equal in free space, vp = vg = c, constant. By contrast, for particles, where causality is due to particle interactions having rest mass mo > 0, we have to employ the Klein-Gordon equation with s2=c2t2−x2−y2−z2+mo2c2. Now special relativity requires a complication: *** = c2 where vg c and therefore vp > c. In the volume outside the cones, causality due to light interactions cannot extend beyond the cones. However, since vp > c and even vp >> c when wavelength λ is long, extreme phase velocities are then limited in their causal effects by the particle uncertainty σ,

关键词： Event Horizon Scattering Range Wave Packet Phase Velocity Group Velocity Dispersion Dynamics Quantum Physics

Kikuchi-Fuj.moto Disease: A case of Lymphadenitis Following COVID-19 Infection

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Open j.urnal of Rheumatology and Autoimmune Diseases 2024年第3期14卷 118-124页

作者： j.spreet Dhillon Bhagvat j. Maheta Neeladri Misra Department of Internal Medicine Sutter Roseville Medical Center Roseville CA USA california Northstate University College of Medicine Elk Grove CA USA

Introduction: Kikuchi-Fuj.moto disease (KFD), also known as histiocytic necrotizing lymphadenitis, is a rare disease of uncertain origin proposed to be secondary to viral or autoimmune causes. It presents as unilateral cervical lymphadenopathy and fever, typically resolving within a few months, however, it mimics malignant lymphoma, leading to extensive work-up fearing malignancy. case History: A 33-year-old female with a history of Sj.gren’s syndrome, rheumatoid arthritis (not on immunosuppressive therapy) and recent COVID-19 infection two months ago presented with episodes of flu-like symptoms;fever (101˚F), chills, and myalgias for two months. Upon evaluation, she had leukopenia (WBC 1.8 k/uL), neutropenia (1.0 k/uL), elevated CRP (134 mg/L), and CT neck demonstrated multiple enlarged cervical lymph nodes with necrosis. The patient was started on Cefdinir and doxycycline for a possible atypical infection given neutropenic fevers and the patient continued to have fevers. A biopsy showed focal necrosis with no evidence of malignancy, suggesting KFD that was likely triggered by a recent COVID infection. She was treated with Prednisone and naproxen, which led to an improvement in symptoms and recovery of her pancytopenia. Discussion: This case is unique since the patient’s recent infection with COVID-19 may have triggered the clinical manifestations of KFD. There have been a few case reports of children who were diagnosed with KFD after a COVID-19 infection and adults diagnosed with KFD following COVID vaccinations;however, this is the first case report involving a young adult in her thirties who was diagnosed with KFD two months after COVID-19.

关键词： Kikuchi-Fuj.moto Disease COVID-19 Rheumatology

Clinical and Demographic Profile of Women with Uterine Fibroids Living in Puerto Rico

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Open j.urnal of Obstetrics and Gynecology 2024年第9期14卷 1347-1362页

作者： Edwin Y. Soto-Velázquez Alexander j. j.ramillo-cañas Shania N. Aponte-Paris Gabriela V. Martínez-Marrero Irazu S. Guinan Gabrielle A. Rivera-Maldonado Alexandra Novas Pedro L. Cruz-Rosa Idhaliz Flores-caldera Maricarmen Colón-Diaz Department of Physiology and Pathology San Juan Bautista School of Medicine Caguas Puerto Rico United States Ponce Research Institute Ponce Health Sciences University Ponce Puerto Rico United States

Introduction: Uterine leiomyomas, or fibroids, are prevalent benign tumors affecting up to 70% of reproductive-age women in the United States, significantly impacting productivity and quality of life. Despite their commonality, the epidemiology and clinical patterns of leiomyomas in Puerto Rico remain inadequately researched. Methods: This study conducted a secondary data analysis using clinical, menstrual cycle characteristics, and demographic data from self-administered questionnaires of women undergoing diagnostic laparoscopy for endometriosis in Puerto Rico. Chi-square tests and t-tests analyzed categorical and continuous variables, respectively (p Results: Among 1,610 endometriosis cases, 312 included uterine fibroids. Prevalence estimates were 10.3% (40 years). Primiparous women averaged 22.14 years, with 40.71% having 2 - 3 pregnancies and 26.28% experiencing miscarriages. Symptoms included infertility (29.5%), dyspareunia (40.7%), severe pain (50%), and dysmenorrhea (75.6%). Comorbidities included ovarian cysts (52.2%) and abnormal uterine bleeding (37.8%). Conclusions: Advanced age, parity, and comorbidities like diabetes and hypertension were prevalent in our cohort. Understanding the epidemiological profile of women living in Puerto Rico with uterine fibroids is crucial for improving diagnostic awareness and enhancing patient care.

关键词： Uterine Fibroids Puerto Rico Epidemiology Dysmenorrhea Abnormal Uterine Bleeding

Reply to the note by Li Piani et al.

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Defence Technology（防务技术） 2024年第1期31卷 603-606页

作者： T.Li Piani j.Weerheij. L.j.Sluys TU Delft Stevinweg 12628 CNDelftthe Netherlands TNO PO Box 452280 AARijswijkthe Netherlands NLDA Faculty of Military Sciences1781 CADen Helderthe Netherlands

In 2017,a ballistic phenomenological model was proposed by the authors of Ref.[1] to numerically simulate the experimental depths of small caliber proj.ctiles impacting walls made of *** opportunity for a new model in the field revealed from the observation that two older models recently used by the authors of Ref.[2] shared a linear relationship between the penetration depth P and the impacting velocity v_(O).

关键词： Penetration Adobe Modeling

Physical Simulation of Thermally Induced Martensite Formation from Retained Austenite in TRIP Steels

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j.urnal of Materials Science & Technology 2003年第Z1期19卷 105-108页

作者： Lie ZHAO fred j. VERMOLEN j.lt SIETSMA Sybrand van der ZWAAG Netherlands Institute for Metals Research P.O.Box 5008 2600 GA Delft The Netherlands Department of Materials Science Delft University of Technology R otterdamseweg 137 2628 AL Delft The Netherlands Department of Applied Mathematics Delft University of Technology Mekelweg 4 2628 CD Delft The Netherlands Department of Materials ScienceDelft University of TechnologyRotterdamseweg 1372628 AL DelftThe Netherlands Netherlands Institute for Metals Research P.O.Box 5008 2600 GA Delft The Netherlands Faculty of Aerospace Engineering Delft University of Technology Kluyverweg 1 2629 HS Delft The Netherlands

The present work analyses the total free energy of the material during the martensitic transformation. A general expression for the martensite fraction as a function of temperature is derived, assuming that the nonchemical free energyis proportional to the volume of martensite. This expression indicates that the temperature-dependent martensitefraction can be predicted once the characteristic transformation temperatures and the relation between the chemicalfree energy and temperature of the martensite and austenite are known. An advantage of this development is thatthe proposed equation is valid for all types of relations between the chemical free energy and temperature. Thissimulation is successfully applied to the martensitic transformation upon further cooling of retained austenite in alow-alloyed TRIP steel, in which the relation between chemical free energy and temperature is quadratic and thefraction is determined from a thermo-magnetic measurement.

关键词： Thermodynamics, Martensitic transformation, Retained austenite, TRIP steels.

Universal optimality of digital nets and lattice designs

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Science China Mathematics 2009年第11期52卷 2309-2320页

作者： HICKERNELL fred j Department of Applied Mathematics Illinois Institute of Technology

This article considers universal optimality of digital nets and lattice designs in a regression model. Based on the equivalence theorem for matrix means and maj.rization theory,the necessary and sufficient conditions for lattice designs being φp-and universally optimal in trigonometric function and Chebyshev polynomial regression models are obtained. It is shown that digital nets are universally optimal for both complete and incomplete Walsh function regression models under some specified conditions,and are also universally optimal for complete Haar wavelet regression models but may not for incomplete Haar wavelet regression models.

关键词： Chebyshev polynomial Haar wavelet Trigonometric function Walsh function 62K15 62K10

Primary and Secondary Microplastic and Nanoplastic Regulations: Perspectives on Water Industry Impacts

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j.urnal of Environmental Protection 2024年第6期15卷 697-715页

作者： Shirin Estahbanati Giridhar Upadhyaya Martha j. M. Wells Katherine Y. Bell Brown and caldwell New York NY USA Brown and caldwell Irvine CA USA EnviroChem Services Cookeville TN USA Brown and caldwell Nashville TN USA

Plastic pollution, both primary and secondary, is an environmental challenge, prompting regulatory actions at global and regional levels. With increasing research about the impacts of micro- and nanoplastics on ecosystems and human health, governments worldwide have undertaken efforts to address this issue. The global community has advanced regulatory efforts that have led to the implementation of national laws or regulations in numerous countries. These measures ban or restrict the use of primary and secondary microplastics and nanoplastics. An overview of global and European regulatory frameworks is presented to provide context for the United States (US). In the endeavor to document plastics regulation development in the US, a description of regulatory agencies and their roles in advancing policy and rules as well as future direction and areas for improvement in regulating plastics are introduced. A discussion of what emerging regulations mean to utilities and industries is also provided along with a comparison of regulatory frameworks.

关键词： Microplastic Regulation Environmental Governance Plastic Pollution Mitigation Regulatory Framework

Universally consistent estimation for stochastic regression models

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Chinese Science Bulletin 1995年第10期40卷 802-807页

作者：安鸿志 Hickernell fred j. 朱力行 Probability Lab Institute of Applied Mathematics Chinese Academy of Sciences Beijing 100080 China Department of Matbematice Hong Kong Baptist University Hong Kong.

Addressed problem Consider multivarate lincar regression model in which x is pdimensional random

关键词： multivariate regression model characteristic function consistency of estimation.

A REDUCED ORDER SCHWARZ METHOD FOR NONLINEAR MULTIScaLE ELLIPTIC EQUATIONS BASED ON TWO-LAYER NEURAL NETWORKS

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j.urnal of Computational Mathematics 2024年第2期42卷 570-596页

作者： Shi Chen Zhiyan Ding Qin Li Stephen j.Wright Mathematics Department University of Wisconsin-MadisonMadisonWI 53706USA Department of Mathematics University of California-BerkeleyBerkeley CA 94720USA Mathematics Department and Discovery Institute University of Wisconsin-Madison MadisonWI 53706USA Computer Sciences Department University of WisconsinMadisonWI 53706USA

Neural networks are powerful tools for approximating high dimensional data that have been used in many contexts,including solution of partial differential equations(PDEs).We describe a solver for multiscale fully nonlinear elliptic equations that makes use of domain decomposition,an accelerated Schwarz framework,and two-layer neural networks to approximate the boundary-to-boundarymap for the subdomains,which is the key step in the Schwarz ***,the boundary-to-boundary map requires solution of boundary-value elliptic problems on each *** leveraging the compressibility of multiscale problems,our approach trains the neural network offline to serve as a surrogate for the usual implementation of the boundary-to-boundary *** method is applied to a multiscale semilinear elliptic equation and a multiscale p-Laplace *** both cases we demonstrate significant improvement in efficiency as well as good accuracy and generalization performance.

关键词： Nonlinear homogenization Multiscale elliptic problem Neural networks Do-main decomposition