“…Part III treats the direct methods of the calculus of variations and their applications to boundary- and eigenvalue-problems for linear and nonlinear partial differential operators. …”
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“……The book that results offers a concise introduction to the subject for students of mathematics, science and engineering who have completed the introductory calculus sequence. …This book is worth a careful look as a candidate text for the next differential equations course you teach.” …”
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“…This second edition has been completely revised and updated and contains a variety of new content and expanded coverage of key topics, such as new exercises on the calculus of distributions, a proof of the Riesz convolution, Steiner symmetrization, and embedding theorems for functions in Sobolev spaces. …”
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“…To accomplish that goal, the authors include a direct derivation of Carleman estimates, the derivation being based essentially on elementary calculus working flexibly for various equations. Because the inverse problem depends heavily on respective equations, too general and abstract an approach may not be balanced. …”
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“…Through the mid-nineteenth century, most American colleges followed a classical curriculum that, in mathematics, rarely reached beyond calculus. With no doctoral programs of any sort in the United States until 1860, mathematical scholarship lagged far behind that in Europe. …”
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“…This monograph is addressed to readers, beginning from the graduate level, with an interest in any of the following: differential equations – ordinary or partial; nonlinear analysis; the calculus of variations; the relationship of minimal surfaces to diffuse interfaces; or the applied mathematics of materials science.…”
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“…The hundreds of meticulously detailed modeling problems were deliberately designed along pedagogical principles found especially effective in the MAA study Characteristics of Successful Calculus Programs, namely, that asking students to work problems that require them to grapple with concepts (or even proofs) and do modeling activities is key to successful student experiences and retention in STEM programs. …”
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“…The text provides a concise exposition of some topics from functional analysis (for instance, C^*-Hilbert modules, K-theory or C^*-bundles, Hermitian K-theory, Fredholm representations, KK-theory, and functional integration) from the theory of differential operators (pseudodifferential calculus and Sobolev chains over C^*-algebras),…”
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“…With the exception of a few more advanced concepts required for the final part of the book, the presentation requires only a knowledge of basic facts from linear algebra, differential equations, and calculus. In addition to classical concepts and ideas, the author covers the stabilization of nonlinear systems using topological methods, realization theory for nonlinear systems, impulsive control and positive systems, the control of rigid bodies, the stabilization of infinite dimensional systems, and the solution of minimum energy problems. …”
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“…Equally suited to classroom use or independent study, the text will appeal to students and professionals alike; only a background in calculus and linear algebra is assumed. Readers looking to continue on to more advanced topics will appreciate the authors’ companion volume Differential Geometry and Lie Groups: A Second Course.…”
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“…We identify-three distinct response patterns, which we name the ‘Agnostic’, the ‘Pragmatic’ and the ‘Sceptic’, and show how the interplay of the salient social identity, personal privacy norms, and the privacy calculus guides the dynamic of privacy decision-making in light of experiential feedback, and the developing public discourse about security risks. …”
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“…Drawing from work that theoretically connects decisions to immigrate legally vs. illegally as well as theoretical insights from literature on the economics of crime, I show how relative probabilities of successful migration using different strategies and relative utility gained using different strategies weigh heavily in immigrants’ calculus. To do so, I use qualitative evidence of migrant strategies in the face of migration policy constraints. …”
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“…CASE PRESENTATION: A 40-year-old man with diabetes type 1 presented to our hospital with diabetic ketoacidosis and abdominal pain initially taken care of in an endocrinology department then transferred to our urology department after discovery on the CT scan of a staghorn calculus in the solitary right kidney is later discovered during the therapeutic management that it is a superior CFRE. …”
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“…The findings of this study unveil a significant correlation between elevated DAS scores and reduced frequency of tooth brushing; calculus removal and appointments for professional teeth cleaning. …”
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“…Chronic periodontitis is the most common type of periodontitis, which is associated with calculus and plaque accumulation. Several studies have indicated that uncured periodontitis can affect the dental pulp. …”
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“…In order to improve the accuracy and universality of the nonlinear viscoelastic-plastic mechanical behavior characterization method of asphalt mixture, a new criterion for the division of the creep process of materials was established based on the strain yield characteristics, and the coexistence mechanism of Viscoelastic–Viscoplastic strain was proposed in the subsequent yield phase; then, a viscoelastic element was constructed in the form of a parallel connection of two fractional viscoelastic elements based on fractional calculus theory, and its mathematical equations were derived; with novel viscoelastic elements, a constitutive model characterizing the whole creep process of asphalt mixtures was developed and its analytical expression was derived. …”
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“…A generalised inflammatory gingival enlargement is most likely a response to local irritants like plaque and calculus but is enhanced by the patient's mouth breathing habit. …”
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“…Other features of Moebius Syndrome include facial nerve paresis, ophthalmoplegias, orthodontic deficiencies (including crowded dentition, swollen and hyperplastic gingiva, dental calculus, etc.), musculoskeletal abnormalities, and impaired mental function. …”
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“…Fractional calculus is an essential tool in studying new phenomena in hydromechanics and heat and mass transfer, particularly anomalous hydromechanical advection–dispersion considering the fractal nature of the porous medium. …”
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“…To understand the strengths and weaknesses of different metagenome profilers, we performed their comprehensive evaluation on simulated metagenomes representing human dental calculus microbiome, with the level of DNA damage successively raised to mimic modern to ancient metagenomes. …”
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