Tingley's problem for a Banach space of Lipschitz functions on the closed unit interval (Research on preserver problems on Banach algebras and related topics)

We prove that every surjective isometry on the unit sphere of Lip(I) of all Lipschitz continuous functions on the closed unit interval I is extended to a surjective real linear isometry on Lip(I) with the norm ∥f∥σ = |f(0)| + ∥f′∥L∞

Third-order integrable difference equations generated by a pair of second-order equations

We show that the third-order difference equations proposed by Hirota, Kimura and Yahagi are generated by a pair of second-order difference equations. In some cases, the pair of the second-order equations are equivalent to the Quispel-Robert-Thomson(QRT) system, but in the other cases, they are irrelevant to the QRT system. We also discuss an ultradiscretization of the equations.Comment: 15 pages, 3 figures; Accepted for Publication in J. Phys.

Discrete mappings with an explicit discrete Lyapunov function related to integrable mappings

We propose discrete mappings of second order that have a discrete analogue of Lyapunov function. The mappings are extensions of the integrable Quispel-Roberts-Thompson (QRT) mapping, and a discrete Lyapunov function of the mappings is identical to an explicit conserved quantity of the QRT mapping. Moreover we can obtain a differential and an ultradiscrete limit of the mappings preserving the existence of Lyapunov function. We also give applications of a mapping with an adjusted parameter, a probabilistic mapping and coupled mappings.Comment: submitted to Physica

Surjective isometries between unitary sets of unital JB∗-algebras

We would like to thank Prof. Lajos Molnár for encouraging us to explore this problem. We are also indebted to the anonymous reviewer for several useful comments. First and fifth authors partially supported by the Spanish Ministry of Science, Innovation and Universities (MICINN) and European Regional Development Fund project no. PGC2018-093332-B-I00, Programa Operativo FEDER 2014-2020 and Consejería de Economía y Conocimiento de la Junta de Andalucía grant numbers A-FQM-242-UGR18 and FQM375. First author partially supported by EPSRC (UK) project “Jordan Algebras, Finsler Geometry and Dynamics” ref. no. EP/R044228/1. Second author partially supported by JSPS KAKENHI Grant Number JP 21J21512. Fourth author partially supported by JSPS KAKENHI (Japan) Grant Number JP 20K03650. * Funding for open access charge: Universidad de Granada / CBUAThis paper is, in a first stage, devoted to establishing a topological–algebraic characterization of the principal component, U0(M), of the set of unitary elements, U(M), in a unital JB⁎-algebra M. We arrive to the conclusion that, as in the case of unital C⁎-algebras, U0(M)=M1−1∩U(M)={Ue⋯Ue(1):n∈N,hj∈Msa∀1≤j≤n}={u∈U(M): there exists w∈U0(M) with ‖u−w‖<2} is analytically arcwise connected. Actually, U0(M) is the smallest quadratic subset of U(M) containing the set eiM. Our second goal is to provide a complete description of the surjective isometries between the principal components of two unital JB⁎-algebras M and N. Contrary to the case of unital C⁎-algebras, we shall deduce the existence of connected components in U(M) which are not isometric as metric spaces. We shall also establish necessary and sufficient conditions to guarantee that a surjective isometry Δ:U(M)→U(N) admits an extension to a surjective linear isometry between M and N, a conclusion which is not always true. Among the consequences it is proved that M and N are Jordan ⁎-isomorphic if, and only if, their principal components are isometric as metric spaces if, and only if, there exists a surjective isometry Δ:U(M)→U(N) mapping the unit of M to an element in U0(N). These results provide an extension to the setting of unital JB⁎-algebras of the results obtained by O. Hatori for unital C⁎-algebras.CBUAConsejería de Economía y Conocimiento de la Junta de Andalucía A-FQM-242-UGR18, FQM375Ministerio de Ciencia, Innovación y UniversidadesEngineering and Physical Sciences Research Council EP/R044228/1Universidad de GranadaMinisterio de Ciencia e InnovaciónJapan Society for the Promotion of Science JP 20K03650, JP 21J21512European Regional Development Fund PGC2018-093332-B-I0

Factors Associated with Remission and/or Regression of Microalbuminuria in Type 2 Diabetes Mellitus

The aim of this study was to clarify the factors associated with the remission and/or regression of microalbuminuria in Japanese patients with type 2 diabetes mellitus. We retrospectively analyzed the data of 130 patients with type 2 diabetes mellitus with microalbuminuria for 2-6 years (3.39±1.31 years). Remission was defined as improving from microalbuminuria to normoalbuminuria using the albumin/creatinine ratio (ACR), and regression of microalbuminuria was defined as a decrease in ACR of 50% or more from baseline. Progression of microalbuminuria was defined as progressing from microalbuminuria to overt proteinuria during the follow-up period. Among 130 patients with type 2 diabetes mellitus with microalbuminuria, 57 and 13 patients were defined as having remission and regression, respectively, while 26 patients progressed to overt proteinuria. Sex (female), higher HDL cholesterol and lower HbA1c were determinant factors associated with remission/regression of microalbuminuria by logistic regression analysis. Lower systolic blood pressure (SBP) was also correlated with remission/regression, but not at a significant level. These results suggest that proper control of blood glucose, BP and lipid profiles may be associated with remission and/or regression of type 2 diabetes mellitus with microalbuminuria in clinical practice

Fermionic solutions of chiral Gross-Neveu and Bogoliubov-de Gennes systems in nonlinear Schr\"odinger hierarchy

The chiral Gross-Neveu model or equivalently the linearized Bogoliubov-de Gennes equation has been mapped to the nonlinear Schr\"odinger (NLS) hierarchy in the Ablowitz-Kaup-Newell-Segur formalism by Correa, Dunne and Plyushchay. We derive the general expression for exact fermionic solutions for all gap functions in the arbitrary order of the NLS hierarchy. We also find that the energy spectrum of the n-th NLS hierarchy generally has n+1 gaps. As an illustration, we present the self-consistent two-complex-kink solution with four real parameters and two fermion bound states. The two kinks can be placed at any position and have phase shifts. When the two kinks are well separated, the fermion bound states are localized around each kink in most parameter region. When two kinks with phase shifts close to each other are placed at distance as short as possible, the both fermion bound states have two peaks at the two kinks, i.e., the delocalization of the bound states occurs.Comment: 7 pages, 1 figure, Phys. Lett. B, in pres

Controlling the Circadian Clock with High Temporal Resolution through Photodosing

Circadian clocks, biological timekeepers that are present in almost every cell of our body, are complex systems whose disruption is connected to various diseases. Controlling cellular clock function with high temporal resolution in an inducible manner would yield an innovative approach for the circadian rhythm regulation. In the present study, we present structure-guided incorporation of photoremovable protecting groups into a circadian clock modifier, longdaysin, which inhibits casein kinase I (CKI). Using photodeprotection by UV or visible light (400 nm) as the external stimulus, we have achieved quantitative and light-inducible control over the CKI activity accompanied by an accurate regulation of circadian period in cultured human cells and mouse tissues, as well as in living zebrafish. This research paves the way for the application of photodosing in achieving precise temporal control over the biological timing and opens the door for chronophotopharmacology to deeper understand the circadian clock system

Reversible modulation of circadian time with chronophotopharmacology

The circadian clock controls daily rhythms of physiological processes. The presence of the clock mechanism throughout the body is hampering its local regulation by small molecules. A photoresponsive clock modulator would enable precise and reversible regulation of circadian rhythms using light as a bio-orthogonal external stimulus. Here we show, through judicious molecular design and state-of-the-art photopharmacological tools, the development of a visible light-responsive inhibitor of casein kinase I (CKI) that controls the period and phase of cellular and tissue circadian rhythms in a reversible manner. The dark isomer of photoswitchable inhibitor 9 exhibits almost identical affinity towards the CKIα and CKIδ isoforms, while upon irradiation it becomes more selective towards CKIδ, revealing the higher importance of CKIδ in the period regulation. Our studies enable long-term regulation of CKI activity in cells for multiple days and show the reversible modulation of circadian rhythms with a several hour period and phase change through chronophotopharmacology

A Point Mutation of Tyr-759 in Interleukin 6 Family Cytokine Receptor Subunit gp130 Causes Autoimmune Arthritis

We generated a mouse line in which the src homology 2 domain–bearing protein tyrosine phosphatase (SHP)-2 binding site of gp130, tyrosine 759, was mutated to phenylalanine (gp130F759/F759). The gp130F759/F759 mice developed rheumatoid arthritis (RA)-like joint disease. The disease was accompanied by autoantibody production and accumulated memory/activated T cells and myeloid cells. Before the disease onset, the T cells were hyperresponsive and thymic selection and peripheral clonal deletion were impaired. The inhibitory effect of IL-6 on Fas ligand expression during activation-induced cell death (AICD) was augmented in gp130F759/F759 T cells in a manner dependent on the tyrosine residues of gp130 required for signal transducer and activator of transcription 3 activation. Finally, we showed that disease development was dependent on lymphocytes. These results provide evidence that a point mutation of a cytokine receptor has the potential to induce autoimmune disease