An optimal gap theorem

By solving the Cauchy problem for the Hodge-Laplace heat equation for $d$-closed, positive $(1, 1)$-forms, we prove an optimal gap theorem for K\"ahler manifolds with nonnegative bisectional curvature which asserts that the manifold is flat if the average of the scalar curvature over balls of radius $r$ centered at any fixed point $o$ is a function of $o(r^{-2})$. Furthermore via a relative monotonicity estimate we obtain a stronger statement, namely a `positive mass' type result, asserting that if $(M, g)$ is not flat, then $\liminf_{r\to \infty} \frac{r^2}{V_o(r)}\int_{B_o(r)}\mathcal{S}(y)\, d\mu(y)>0$ for any $o\in M$

Non-minimal coupling of photons and axions

We establish a new self-consistent system of equations accounting for a non-minimal interaction of gravitational, electromagnetic and axion fields. The procedure is based on a non-minimal extension of the standard Einstein-Maxwell-axion action. The general properties of a ten-parameter family of non-minimal linear models are discussed. We apply this theory to the models with pp-wave symmetry and consider propagation of electromagnetic waves non-minimally coupled to the gravitational and axion fields. We focus on exact solutions of electrodynamic equations, which describe quasi-minimal and non-minimal optical activity induced by the axion field. We also discuss empirical constraints on coupling parameters from astrophysical birefringence and polarization rotation observations.Comment: 31 pages, 2 Tables; replaced with the final version published in Classical and Quantum Gravit

Extended axion electrodynamics: Optical activity induced by nonstationary dark matter

We establish a new self-consistent Einstein-Maxwell-axion model based on the Lagrangian, which is linear in the pseudoscalar (axion) field and its four-gradient and includes the four-vector of macroscopic velocity of the axion system as a whole. We consider extended equations of the axion electrodynamics, modified gravity field equations, and discuss nonstationary effects in the phenomenon of optical activity induced by axions.Comment: 6 pages, 0 figures, accepted for publication in the Journal Gravitation and Cosmology, reported at the 14th Russian Gravitational Conference (Ulyanovsk, 2011

Transition from Mott insulator to superconductor in GaNb4_{4}Se8_{8} and GaTa4_{4}Se8_{8} under high pressure

Electronic conduction in GaM$_{4}$Se$_{8}$ (M=Nb;Ta) compounds with the fcc GaMo$_{4}$S$_{8}$-type structure originates from hopping of localized unpaired electrons (S=1/2) among widely separated tetrahedral M$_{4}$ metal clusters. We show that under pressure these systems transform from Mott insulators to a metallic and superconducting state with T$_{C}$=2.9 and 5.8K at 13 and 11.5GPa for GaNb$_{4}$Se$_{8}$ and GaTa$_{4}$Se$_{8}$, respectively. The occurrence of superconductivity is shown to be connected with a pressure-induced decrease of the MSe$_{6}$ octahedral distortion and simultaneous softening of the phonon associated with MSe-bonds.Comment: 10 pages, 5 figure

Non-ancient solution of the Ricci flow

For any complete noncompact K$\ddot{a}$hler manifold with nonnegative and bounded holomorphic bisectional curvature,we provide the necessary and sufficient condition for non-ancient solution to the Ricci flow in this paper.Comment: seven pages, latex fil

PENGARUH “ SERING CETING ” TERHADAP PENGETAHUAN IBU BALITA TENTANG STUNTING

In East Kalimantan, prevalence of stunting was increasing from 26.7% in 2015 becomes 30.8% in 2018. In 2019 from 10 regencies in East Kalimantan, prevalence in Kutai Kartanegara Regency 19.49% and prevalence in Balikpapan City placed in second to reach 18.48%. Stunting affects cognitive and physic of children, productvity declines, bad health and high risk to degenerative diseases. Survey of this research said that 3 from 5 mothers who has stunting baby, has no knowladge of stunting and what stunting is, meanwhile knowladge significantly effect on prevention and treatment stunting. There is an inovation of transfer knowladge about stunting called “SerInG CeTing” which is unapplied in Health center of Baru Tengah so that the researcher want to analysis the effect of “SerInG CeTing”.  This research used quasi eksperimen dengan one group pre-post test without control group design. Purpose of this research to influance analysis of “SerInG CeTing” on Mothers. The sampling technique used total sampling with 38 mothers who have stunting toddler in Health Center of Baru Tengah in Mei 2022. The result of this research “SerInG CeTing” is one of inovation which significanly increasing knowladge of mother in stunting with p value 0.000 < 0.05

Scattering of relativistic particles with Aharonov-Bohm-Coulomb interaction in two dimensions

The Aharonov-Bohm-Coulomb potentials in two dimensions may describe the interaction between two particles carrying electric charge and magnetic flux, say, Chern--Simons solitons, or so called anyons. The scattering problem for such two-body systems is extended to the relativistic case, and the scattering amplitude is obtained as a partial wave series. The electric charge and magnetic flux is ($-q$, $-\phi/Z$) for one particle and ($Zq$, $\phi$) for the other. When $(Zq^2/\hbar c)^2\ll 1$, and $q\phi/2\pi\hbar c$ takes on integer or half integer values, the partial wave series is summed up approximately to give a closed form. The results exhibit some nonperturbative features and cannot be obtained from perturbative quantum electrodynamics at the tree level.Comment: revtex, 11 pages, no figur

New selection rules for resonant Raman scattering on quantum wires

The bosonisation technique is used to calculate the resonant Raman spectrum of a quantum wire with two electronic sub-bands occupied. Close to resonance, the cross section at frequencies in the region of the inter sub-band transitions shows distinct peaks in parallel polarisation of the incident and scattered light that are signature of collective higher order spin density excitations. This is in striking contrast to the conventional selection rule for non-resonant Raman scattering according to which spin modes can appear only in perpendicular polarisation. We predict a new selection rule for the excitations observed near resonance, namely that, apart from charge density excitations, only spin modes with positive group velocities can appear as peaks in the spectra in parallel configuration close to resonance. The results are consistent with all of the presently available experimental data.Comment: 7 pages, 2 figure