Strings at future singularities

We discuss the behaviour of strings propagating in spacetimes which allow future singularities of either a sudden future or a Big-Rip type. We show that in general the invariant string size remains finite at sudden future singularities while it grows to infinity at a Big-Rip. This claim is based on the discussion of both the tensile and null strings. In conclusion, strings may survive a sudden future singularity, but not a Big-Rip where they are infinitely stretched.Comment: REVTEX 4.0, 4 pages, no figures, references adde

Lineability, spaceability, and additivity cardinals for Darboux-like functions

We introduce the concept of maximal lineability cardinal number, mL(M), of a subset M of a topological vector space and study its relation to the cardinal numbers known as: additivity A(M), homogeneous lineability HL(M), and lineability L(M) of M. In particular, we will describe, in terms of L, the lineability and spaceability of the families of the following Darboux-like functions on R-n, n >= 1: extendable, Jones, and almost continuous function

Generalized gradients on Lie algebroids

Generalized O(n) -gradients for connections on Lie algebroids are derived

An undecidable case of lineability in R^R

Recently it has been proved that, assuming that there is an almost disjoint family of cardinality (2^{\mathfrak c}) in (\mathfrak c) (which is assured, for instance, by either Martin's Axiom, or CH, or even 2^{<\mathfrak c=\mathfrak c}) one has that the set of Sierpi\'nski-Zygmund functions is (2^{\mathfrak{c}})-strongly algebrable (and, thus, (2^{\mathfrak{c}})-lineable). Here we prove that these two statements are actually equivalent and, moreover, they both are undecidable. This would be the first time in which one encounters an undecidable proposition in the recently coined theory of lineability.Comment: 5 page

Polycythemia vera as a presentation of renal angiomyolipoma: a case report

<p>Abstract</p> <p>Introduction</p> <p>Angiomyolipoma is a common benign renal tumor composed of thick-walled blood vessels, smooth muscle, and adipose tissue. It may be found incidentally during workup for suspected renal disease. Although angiomyolipoma may present as a palpable, tender renal mass with flank pain and gross or microscopic hematuria, many patients are asymptomatic. Erythrocytosis is an unusual presentation, and malignant transformation may be suspected. This report describes a rare case of a woman diagnosed with renal angiomyolipoma and polycythemia vera. The report discusses the differential diagnosis using erythropoietin, erythropoietin-receptor and Janus kinase 2.</p> <p>Case presentation</p> <p>A 79-year-old Chinese woman was diagnosed with erythrocytosis according to World Health Organization criteria. An upper left renal pole angiomyolipoma was successfully ablated after multiple phlebotomy treatments. Red cell count immediately returned to normal, but gradually increased after 4 months. Polycythemia vera was finally diagnosed by positive mutation of Janus kinase 2 and negative erythropoietin protein expression. Her clinical symptoms improved with regular phlebotomy and hydroxyurea treatment.</p> <p>Conclusion</p> <p>Concurrent occurence of angiomyolipoma and polycythemia vera is rare. Polycythemia vera can be easily missed. Polycythemia vera can be confirmed with high specificity and sensitivity by the acquired somatic mutation. Surgical intervention for this renal tumor should be avoided unless malignancy or renal cell carcinoma is suspected or to prevent spontaneous rupture of larger tumors.</p

Domain wall brane in squared curvature gravity

We suggest a thick braneworld model in the squared curvature gravity theory. Despite the appearance of higher order derivatives, the localization of gravity and various bulk matter fields is shown to be possible. The existence of the normalizable gravitational zero mode indicates that our four-dimensional gravity is reproduced. In order to localize the chiral fermions on the brane, two types of coupling between the fermions and the brane forming scalar is introduced. The first coupling leads us to a Schr\"odinger equation with a volcano potential, and the other a P\"oschl-Teller potential. In both cases, the zero mode exists only for the left-hand fermions. Several massive KK states of the fermions can be trapped on the brane, either as resonant states or as bound states.Comment: 18 pages, 5 figures and 1 table, references added, improved version to be published in JHE

Screening of cosmological constant for De Sitter Universe in non-local gravity, phantom-divide crossing and finite-time future singularities

We investigate de Sitter solutions in non-local gravity as well as in non-local gravity with Lagrange constraint multiplier. We examine a condition to avoid a ghost and discuss a screening scenario for a cosmological constant in de Sitter solutions. Furthermore, we explicitly demonstrate that three types of the finite-time future singularities can occur in non-local gravity and explore their properties. In addition, we evaluate the effective equation of state for the universe and show that the late-time accelerating universe may be effectively the quintessence, cosmological constant or phantom-like phases. In particular, it is found that there is a case in which a crossing of the phantom divide from the non-phantom (quintessence) phase to the phantom one can be realized when a finite-time future singularity occurs. Moreover, it is demonstrated that the addition of an $R^2$ term can cure the finite-time future singularities in non-local gravity. It is also suggested that in the framework of non-local gravity, adding an $R^2$ term leads to possible unification of the early-time inflation with the late-time cosmic acceleration.Comment: 42 pages, no figure, version accepted for publication in General Relativity and Gravitatio

Reconstruction of the equation of state for the cyclic universes in homogeneous and isotropic cosmology

We study the cosmological evolutions of the equation of state (EoS) for the universe in the homogeneous and isotropic Friedmann-Lema\^{i}tre-Robertson-Walker (FLRW) space-time. In particular, we reconstruct the cyclic universes by using the Weierstrass and Jacobian elliptic functions. It is explicitly illustrated that in several models the universe always stays in the non-phantom (quintessence) phase, whereas there also exist models in which the crossing of the phantom divide can be realized in the reconstructed cyclic universes.Comment: 29 pages, 8 figures, version accepted for publication in Central European Journal of Physic

(Photo)physical properties of new molecular glasses end-capped with thiophene rings composed of diimide and imine units

New symmetrical arylene bisimide derivatives formed by using electron-donating-electron-accepting systems were synthesized. They consist of a phthalic diimide or naphthalenediimide core and imine linkages and are end-capped with thiophene, bithiophene, and (ethylenedioxy)thiophene units. Moreover, polymers were obtained from a new diamine, N,N′-bis(5- aminonaphthalenyl)naphthalene-1,4,5,8-dicarboximide and 2,5- thiophenedicarboxaldehyde or 2,2′-bithiophene-5,5′-dicarboxaldehyde. The prepared azomethine diimides exhibited glass-forming properties. The obtained compounds emitted blue light with the emission maximum at 470 nm. The value of the absorption coefficient was determined as a function of the photon energy using spectroscopic ellipsometry. All compounds are electrochemically active and undergo reversible electrochemical reduction and irreversible oxidation processes as was found in cyclic voltammetry and differential pulse voltammetry (DPV) studies. They exhibited a low electrochemically (DPV) calculated energy band gap (Eg) from 1.14 to 1.70 eV. The highest occupied molecular orbital and lowest unoccupied molecular orbital levels and Eg were additionally calculated theoretically by density functional theory at the B3LYP/6-31G(d,p) level. The photovoltaic properties of two model compounds as the active layer in organic solar cells in the configuration indium tin oxide/poly(3,4-(ethylenedioxy)thiophene):poly(styrenesulfonate)/active layer/Al under an illumination of 1.3 mW/cm2 were studied. The device comprising poly(3-hexylthiophene) with the compound end-capped with bithiophene rings showed the highest value of Voc (above 1 V). The conversion efficiency of the fabricated solar cell was in the range of 0.69-0.90%

f(R) theories

Over the past decade, f(R) theories have been extensively studied as one of the simplest modifications to General Relativity. In this article we review various applications of f(R) theories to cosmology and gravity - such as inflation, dark energy, local gravity constraints, cosmological perturbations, and spherically symmetric solutions in weak and strong gravitational backgrounds. We present a number of ways to distinguish those theories from General Relativity observationally and experimentally. We also discuss the extension to other modified gravity theories such as Brans-Dicke theory and Gauss-Bonnet gravity, and address models that can satisfy both cosmological and local gravity constraints.Comment: 156 pages, 14 figures, Invited review article in Living Reviews in Relativity, Published version, Comments are welcom