A stability version of H\"older's inequality

We present a stability version of H\"older's inequality, incorporating an extra term that measures the deviation from equality. Applications are given.Comment: Journal of Mathematical Analysis and Applications, Volume 343, Issue 2, Pages 842-852. This version differs from the published one in that it contains a new reference, and a trivial improvement of Corollary 3.2. fo

Local Index Formula on the Equatorial Podles Sphere

We discuss spectral properties of the equatorial Podles sphere. As a preparation we also study the `degenerate' (i.e. $q=0$) case (related to the quantum disk). We consider two different spectral triples: one related to the Fock representation of the Toeplitz algebra and the isopectral one. After the identification of the smooth pre-$C^*$-algebra we compute the dimension spectrum and residues. We check the nontriviality of the (noncommutative) Chern character of the associated Fredholm modules by computing the pairing with the fundamental projector of the $C^*$-algebra (the nontrivial generator of the $K_0$-group) as well as the pairing with the $q$-analogue of the Bott projector. Finally, we show that the local index formula is trivially satisfied.Comment: 18 pages, no figures; minor correction

ANTIBACTERIAL EFFECTS OF SINGLE AND COMBINED CRUDE EXTRACTS OF SYNADENIUM GLAUCESCENS AND COMMIPHORA SWYNNERTONII

Background: Synadenium glaucescens and Commiphora swynnertonii are among the reported plants used traditionally for treatment of bacterial infections. This study reports antibacterial effects of single and combined extracts from leaves, stem and root barks of Commiphora swynnertonii and Synadenium glaucescens. Materials and Methods: Plants were collected from Manyara and Njombe regions in Tanzania. Extraction was done using dichloromethane and methanol. The extracts were assessed for antibacterial activity against Gram-positive bacteria (Staphylococcus aureus and Enterococcus faecalis) and Gram-negative bacteria (Escherichia coli, Klebsiella pneumonia and Pseudomonas aeruginosa). Minimum Inhibitory Concentrations (MIC) was determined by broth microdilution, while Fractional Inhibitory Concentration (FIC) indices were calculated from MIC values of combined extracts to determine combination effects. Results: Strong antibacterial activities were demonstrated by all extracts of S. glaucescens (MIC 0.011-0.375mg/mL) against Gram-positive bacteria and methanol extracts of C. swynnertonii (MIC 0.047-0.375mg/mL). Synergistic effect was observed when combining methanol extracts of C. swynnertonii stem bark with S. glaucescens leaves against S. aureus (∑FIC 0.5), Other synergistic effects were observed against E. faecalis with dichloromethane extracts of C. swynnertonii stem bark and S. glaucescens stem bark (∑FIC 0.5), and C. swynnertonii root bark and S. glaucescens root bark (FIC index 0.3). For the remaining combinations, mainly additive effects were observed. Conclusion: Synergistic effects on bacteria were observed by combining different plant parts of S. glaucescens and C. swynnertonii suggesting that it could be beneficial to combine such extracts when used for antibacterial purposes

Differential pain-related behaviors and bone disease in immunocompetent mouse models of myeloma

Bone pain is a serious and debilitating symptom of multiple myeloma (MM) that impairs the quality of life of patients. The underlying mechanisms of the pain are unknown and understudied, and there is a need for immunocompetent preclinical models of myeloma‐induced bone pain. The aim of this study was to provide the first in‐depth behavioral characterization of an immunocompetent mouse model of MM presenting the clinical disease features: osteolytic bone disease and bone pain. We hypothesized that a widely used syngeneic model of MM, established by systemic inoculation of green fluorescent protein‐tagged myeloma cells (5TGM1‐GFP) in immunocompetent C57Bl/KaLwRijHsd (BKAL) mice, would present pain‐related behaviors. Disease phenotype was confirmed by splenomegaly, high serum paraprotein, and tumor infiltration in the bone marrow of the hind limbs; however, myeloma‐bearing mice did not present pain‐related behaviors or substantial bone disease. Thus, we investigated an alternative model in which 5TGM1‐GFP cells were directly inoculated into the intrafemoral medullary cavity. This localized myeloma model presented the hallmarks of the disease, including high serum paraprotein, tumor growth, and osteolytic bone lesions. Compared with control mice, myeloma‐bearing mice presented myeloma‐induced pain‐related behaviors, a phenotype that was reversed by systemic morphine treatment. Micro‐computed tomography analyses of the myeloma‐inoculated femurs showed bone disease in cortical and trabecular bone. Repeated systemic bisphosphonate treatment induced an amelioration of the nociceptive phenotype, but did not completely reverse it. Furthermore, intrafemorally injected mice presented a profound denervation of the myeloma‐bearing bones, a previously unknown feature of the disease. This study reports the intrafemoral inoculation of 5TGM1‐GFP cells as a robust immunocompetent model of myeloma‐induced bone pain, with consistent bone loss. Moreover, the data suggest that myeloma‐induced bone pain is caused by a combinatorial mechanism including osteolysis and bone marrow denervation. © 2019 The Authors. JBMR Plus published by Wiley Periodicals, Inc. on behalf of American Society for Bone and Mineral Research

Branes, Anti-Branes and Brauer Algebras in Gauge-Gravity duality

We propose gauge theory operators built using a complex Matrix scalar which are dual to brane-anti-brane systems in $AdS_5 \times S^5$, in the zero coupling limit of the dual Yang-Mills. The branes involved are half-BPS giant gravitons. The proposed operators dual to giant-anti-giant configurations satisfy the appropriate orthogonality properties. Projection operators in Brauer algebras are used to construct the relevant multi-trace Matrix operators. These are related to the ``coupled representations'' which appear in 2D Yang-Mills theory. We discuss the implications of these results for the quantum mechanics of a complex matrix model, the counting of non-supersymmetric operators and the physics of brane-anti-brane systems. The stringy exclusion principle known from the properties of half-BPS giant gravitons, has a new incarnation in this context. It involves a qualitative change in the map between brane-anti-brane states to gauge theory operators. In the case of a pair of sphere giant and anti-giant this change occurs when the sum of the magnitudes of their angular momenta reaches $N$.Comment: 52 pages, 10 figure

Geometric K-Homology of Flat D-Branes

We use the Baum-Douglas construction of K-homology to explicitly describe various aspects of D-branes in Type II superstring theory in the absence of background supergravity form fields. We rigorously derive various stability criteria for states of D-branes and show how standard bound state constructions are naturally realized directly in terms of topological K-cycles. We formulate the mechanism of flux stabilization in terms of the K-homology of non-trivial fibre bundles. Along the way we derive a number of new mathematical results in topological K-homology of independent interest.Comment: 45 pages; v2: References added; v3: Some substantial revision and corrections, main results unchanged but presentation improved, references added; to be published in Communications in Mathematical Physic

Role of quantum statistics in the photoassociation of Bose-Einstein condensates

We show that the photoassociation of an atomic Bose-Einstein condensate to form condensed molecules is a chemical process which not only does not obey the Arrhenius rules for chemical reactions, but that it can also depend on the quantum statistics of the reactants. Comparing the predictions of a truncated Wigner representation for different initial quantum states, we find that, even when the quantum prediction for an initial coherent state is close to the Gross-Pitaevskii prediction, other quantum states may result in very different dynamics

Quantum superchemistry: Role of trapping profile and quantum statistics

The process of Raman photoassociation of a trapped atomic condensate to form condensed molecules has been labeled superchemistry because it can occur at 0 K and experiences coherent bosonic stimulation. We show here that the differences from ordinary chemical processes go even deeper, with the conversion rates depending on the quantum state of the reactants, as expressed by the Wigner function. We consider different initial quantum states of the trapped atomic condensate and different forms of the confining potentials, demonstrating the importance of the quantum statistics and the extra degrees of freedom which massive particles and trapping potentials make available over the analogous optical process of second-harmonic generation. We show that both mean-field analyses and quantum calculations using an inappropriate initial condition can make inaccurate predictions for a given system. This is possible whether using a spatially dependent analysis or a zero-dimensional approach as commonly used in quantum optics