Stable directions for small nonlinear Dirac standing waves

We prove that for a Dirac operator with no resonance at thresholds nor eigenvalue at thresholds the propagator satisfies propagation and dispersive estimates. When this linear operator has only two simple eigenvalues close enough, we study an associated class of nonlinear Dirac equations which have stationary solutions. As an application of our decay estimates, we show that these solutions have stable directions which are tangent to the subspaces associated with the continuous spectrum of the Dirac operator. This result is the analogue, in the Dirac case, of a theorem by Tsai and Yau about the Schr\"{o}dinger equation. To our knowledge, the present work is the first mathematical study of the stability problem for a nonlinear Dirac equation.Comment: 62 page

Product factorability of integral bilinear operators on Banach function spaces

[EN] This paper deals with bilinear operators acting in pairs of Banach function spaces that factor through the pointwise product. We find similar situations in different contexts of the functional analysis, including abstract vector lattices¿orthosymmetric maps, C¿-algebras¿zero product preserving operators, and classical and harmonic analysis¿integral bilinear operators. Bringing together the ideas of these areas, we show new factorization theorems and characterizations by means of norm inequalities. The objective of the paper is to apply these tools to provide new descriptions of some classes of bilinear integral operators, and to obtain integral representations for abstract classes of bilinear maps satisfying certain domination properties.The first author was supported by TUBITAK-The Scientific and Technological Research Council of Turkey, Grant No. 2211/E. The second author was supported by Ministerio de Economia y Competitividad (Spain) and FEDER, Grant MTM2016-77054-C2-1-P.Erdogan, E.; Sánchez Pérez, EA.; Gok, O. (2019). Product factorability of integral bilinear operators on Banach function spaces. Positivity. 23(3):671-696. https://doi.org/10.1007/s11117-018-0632-zS671696233Abramovich, Y.A., Kitover, A.K.: Inverses of Disjointness Preserving Operators. American Mathematical Society, Providence (2000)Abramovich, Y.A., Wickstead, A.W.: When each continuous operator is regular II. Indag. Math. (N.S.) 8(3), 281–294 (1997)Alaminos, J., Brešar, M., Extremera, J., Villena, A.R.: Maps preserving zero products. Studia Math. 193(2), 131–159 (2009)Alaminos, J., Brešar, M., Extremera, J., Villena, A.R.: On bilinear maps determined by rank one idempotents. Linear Algebra Appl. 432, 738–743 (2010)Alaminos, J., Extremera, J., Villena, A.R.: Orthogonality preserving linear maps on group algebras. Math. Proc. Camb. Philos. Soc. 158, 493–504 (2015)Ben Amor, F.: On orthosymmetric bilinear maps. Positivity 14, 123–134 (2010)Astashkin, S.V., Maligranda, L.: Structure of Cesàro function spaces: a survey. Banach Center Publ. 102, 13–40 (2014)Beckenstein, E., Narici, L.: A non-Archimedean Stone–Banach theorem. Proc. Am. Math. Soc. 100(2), 242–246 (1987)Bu, Q., Buskes, G., Kusraev, A.G.: Bilinear maps on products of vector lattices: a survey. In: Boulabiar, K., Buskes, G., Triki, A. (eds.) Positivity: Trends in Mathematics, pp. 97–126. Springer, Birkhuser (2007)Buskes, G., van Rooij, A.: Almost f-algebras: commutativity and Cauchy–Schwarz inequality. Positivity 4, 227–231 (2000)Buskes, G., van Rooij, A.: Squares of Riesz spaces. Rocky Mt. J. Math. 31(1), 45–56 (2001)Calabuig, J.M., Delgado, O., Sánchez Pérez, E.A.: Generalized perfect spaces. Indag. Math. (N.S.) 19(3), 359–378 (2008)Calderón, A.P.: Intermediate spaces and interpolation, the complex method. Studia Math. 24, 113–190 (1964)Defant, A.: Variants of the Maurey-Rosenthal theorem for quasi Köthe function spaces. Positivity 5, 153–175 (2001)Delgado Garrido, O., Sánchez Pérez, E.A.: Strong factorizations between couples of operators on Banach function spaces. J. Convex Anal. 20(3), 599–616 (2013)Diestel, J., Jarchow, H., Tonge, A.: Absolutely Summing Operators, vol. 43. Cambridge University Press, Cambridge (1995)Erdoğan, E., Calabuig, J.M., Sánchez Pérez, E.A.: Convolution-continuous bilinear operators acting in Hilbert spaces of integrable functions. Ann. Funct. Anal. 9(2), 166–179 (2018)Diestel, J., Uhl, J.J.: Vector Measures. American Mathematical Society, Providence (1977)Fremlin, D.H.: Tensor products of Archimedean vector lattices. Am. J. Math. 94, 778–798 (1972)Gillespie, T.A.: Factorization in Banach function spaces. Nederl. Akad. Wetensch. Indag. Math. 43(3), 287–300 (1981)Grafakos, L., Li, X.: Uniform bounds for the bilinear Hilbert transforms I. Ann. Math. 159, 889–933 (2004)Kantorovich, K.L., Akilov, G.P.: Functional Analysis, Nauka, Moscow 1977 (Russian). English transl. Pergamon Press, Oxford, Elmsford, New York (1982)Kolwicz, P., Leśnik, K., Maligranda, L.: Pointwise products of some Banach function spaces and factorization. J. Funct. Anal. 266(2), 616–659 (2014)Kolwicz, P., Leśnik, K.: Topological and geometrical structure of Calderón–Lozanovskii construction. Math. Inequal. Appl. 13(1), 175–196 (2010)Kühn, B.: Banachverbände mit ordnungsstetiger dualnorm. Math. Z. 167(3), 271–277 (1979)Lindenstrauss, J., Tzafriri, L.: Classical Banach Spaces II: Function Spaces, vol. 97. Springer, Berlin (1979)Lozanovskii, G.Ya.: On some Banach lattices. Sibirsk. Mat. Zh. 10, 584-599 (1969)(Russian)English transl. in Siberian Math. J. 10(3), 419-431 (1969)Maligranda, L., Persson, L.E.: Generalized duality of some Banach function spaces. Nederl. Akad. Wetensch. Indag. 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Marine anticancer agents: An overview with a particular focus on their chemical classes

UID/Multi/04378/2019 IF/00700/2014 grant number 216Z167 grant RTA 2015-00010-C03-02 No. PBA/MB/16/01 PDOC/19/02/01The marine environment is a rich source of biologically active molecules for the treatment of human diseases, especially cancer. The adaptation to unique environmental conditions led marine organisms to evolve different pathways than their terrestrial counterparts, thus producing unique chemicals with a broad diversity and complexity. So far, more than 36,000 compounds have been isolated from marine micro- and macro-organisms including but not limited to fungi, bacteria, microalgae, macroalgae, sponges, corals, mollusks and tunicates, with hundreds of new marine natural products (MNPs) being discovered every year. Marine-based pharmaceuticals have started to impact modern pharmacology and different anti-cancer drugs derived from marine compounds have been approved for clinical use, such as: cytarabine, vidarabine, nelarabine (prodrug of ara-G), fludarabine phosphate (pro-drug of ara-A), trabectedin, eribulin mesylate, brentuximab vedotin, polatuzumab vedotin, enfortumab vedotin, belantamab mafodotin, plitidepsin, and lurbinectedin. This review focuses on the bioactive molecules derived from the marine environment with anticancer activity, discussing their families, origin, structural features and therapeutic use.publishersversionpublishe

On non-local variational problems with lack of compactness related to non-linear optics

We give a simple proof of existence of solutions of the dispersion manage- ment and diffraction management equations for zero average dispersion, respectively diffraction. These solutions are found as maximizers of non-linear and non-local vari- ational problems which are invariant under a large non-compact group. Our proof of existence of maximizer is rather direct and avoids the use of Lions' concentration compactness argument or Ekeland's variational principle.Comment: 30 page

Mammary tuberculosis – importance of recognition and differentiation from that of a breast malignancy: report of three cases and review of the literature

<p>Abstract</p> <p>Background</p> <p>While tuberculosis of the breast is an extremely uncommon entity seen in western populations, it accounts for up to 3% of all treatable breast lesions in developing countries.</p> <p>Case presentations</p> <p>We reviewed three female cases of mammary tuberculosis that were diagnosed and treated in Turkey during the same calendar year. All three patients presented with a painful breast mass. In all cases, fine needle aspiration was nondiagnostic for mammary tuberculosis. However, the diagnosis of mammary tuberculosis was confirmed by histopathologic evaluation at the time of open surgical biopsy. All three patients were treated with antituberculous therapy for six months. At the end of the treatment period, each patient appeared to be clinically and radiologically without evidence of residual disease.</p> <p>Conclusion</p> <p>The diagnosis of mammary tuberculosis rests on the appropriate clinical suspicion and the histopathologic findings of the breast lesion. Its recognition and differentiation from that of a breast malignancy is absolutely necessary. Antituberculous chemotherapy, initiated immediately upon diagnosis, forms the mainstay of treatment for mammary tuberculosis.</p

Towards a common measure of greenhouse gas related logistics activity using data envelopment analysis

Monitoring company emissions from freight transport is essential if future greenhouse gas (GHG) reductions are to be realised. Modern economies are characterised increasingly by lower density freight movements. However, weight-based measures of freight transport activity (tonne-kilometre, tonnes lifted) are not good at describing volume-limited freight. After introducing the need for performance measurement, the problem of benchmarking is outlined in more detail. A context-dependent undesirable output data envelopment analysis (DEA) model, designed to be sensitive to business context, is then tested on a simulated set of fleet profiles. DEA can produce more consistent measures of good-practice, compared to ratio-based key performance indicators (KPI), providing emission reduction targets for companies and an aggregate reporting tool

British Valued Life Activities Scale [British VLAs]

Background The Valued Life Activities Scale (VLAs) measures difficulty in daily activities and social participation. With various versions involving a different number of items, we have linguistically and culturally adopted the full VLAs (33-items) and psychometrically tested it in adults with rheumatic and musculoskeletal diseases in the United Kingdom. Methods Participants with Rheumatoid Arthritis, Ankylosing Spondylitis, Chronic Pain/ Fibromyalgia, Chronic Hand/ Upper Limb Conditions, Osteoarthritis, Systemic Lupus, Systemic Sclerosis and Primary Sjogren’s Syndrome were recruited from out-patient clinics in National Health Service Hospitals, General Practice and patient organisations in the UK. Phase1 involved linguistic and cultural adaptation: forward translation to British English; synthesis; expert panel review and cognitive debriefing interviews. In Phase2 participants completed postal questionnaires to assess internal construct validity using (i) Confirmatory Factor Analysis (CFA) (ii) Mokken scaling and (iii) Rasch model. Results Responders (n = 1544) had mean age of 59 years (SD13.3) and 77.2% women. A CFA failed to support a total score from the 33-items (Chi Square 3552:df 464: p < 0.0001). Mokken scaling indicated a strong non-parametric association between items. Fit to the Rasch model indicated that the VLAs was characterised by multidimensionality and item misfit, which may have been influenced by clusters of residual item correlations. An item banking approach resolved a 25-item calibrated set whose application could accommodate the ‘does not apply to me’ response option. Conclusions The UK version of the VLAs failed to satisfy classical and modern psychometric standards for complete item sets. However, as the scale is not usually applied in complete format, an item bank approach calibrated 25 items with fit to the Rasch model. Suitable Computer Adaptive Testing (CAT) software could implement the item set, giving patients the choice of whether an item applies to them, or not

Effect of mixture proportions on the drying shrinkage and permeation properties of high strength concrete containing class F fly ash

Sustainability of concrete can be improved by using large volume of fly ash as a replacement of cement and by ensuring improved durability of concrete. Durability of concrete containing large volume of class F fly ash is dependent on the design of mixture proportions. This paper presents an experimental study on the effect of mixture proportions on the drying shrinkage and permeation properties of high strength concrete containing large volume local class F fly ash. Concrete mixtures were designed with and without adjustments in the water to binder ratio (w/b) and the total binder content to take into account the incorporation of fly ash up to 40% of total binder. Concretes, in which the mixture proportions were adjusted for fly ash inclusion achieved equivalent strength of the control concrete and showed enhanced properties of drying shrinkage, sorptivity, water permeability and chloride penetration as compared to the control concrete. The improvement of durability properties was less significant when no adjustments were made to the w/b ratio and total binder content. The results show the necessity of the adjustments in mixture proportions of concrete to achieve improved durability properties when using class F fly ash as a cement replacement

Loneliness and Social Internet Use: Pathways to Reconnection in a Digital World?

With the rise of online social networking, social relationships are increasingly developed and maintained in a digital domain. Drawing conclusions about the impact of the digital world on loneliness is difficult because there are contradictory findings, and cross-sectional studies dominate the literature, making causation difficult to establish. In this review, we present our theoretical model and propose that there is a bidirectional and dynamic relationship between loneliness and social Internet use. When the Internet is used as a way station on the route to enhancing existing relationships and forging new social connections, it is a useful tool for reducing loneliness. But when social technologies are used to escape the social world and withdraw from the “social pain” of interaction, feelings of loneliness are increased. We propose that loneliness is also a determinant of how people interact with the digital world. Lonely people express a preference for using the Internet for social interaction and are more likely to use the Internet in a way that displaces time spent in offline social activities. This suggests that lonely people may need support with their social Internet use so that they employ it in a way that enhances existing friendships and/or to forge new ones