Abstract:
Electron-positron pair creation in supercritical electric fields limits the net charge of any static, spherical object, such as superheavy nuclei, strangelets, and Q-balls, or compact stars like neutron stars, quark stars, and black holes. For radii between $4\times10^2$ fm and $10^4$ fm the upper bound on the net charge is given by the universal relation $Z=0.71R_{fm}$, and for larger radii (measured in fm or km) $Z = 7 \times 10^{-5} R_{fm}^2 = 7 \times 10^{31} R_{km}^2$. For objects with nuclear density the relation corresponds to $Z \approx 0.7 A^{1/3}$ ($10^{8} < A < 10^{12}$) and $Z \approx 7\times10^{-5} A^{2/3}$ ($A > 10^{12}$), where $A$ is the baryon number. For some systems this universal upper bound improves existing charge limits in the literature.

Abstract:
Electron-positron pair creation in supercritical electric fields limits the net charge of any static, spherical object, such as superheavy nuclei, strangelets, and Q-balls, or compact stars like neutron stars, quark stars, and black holes. For radii between $4\times10^2$ fm and $10^4$ fm the upper bound on the net charge is given by the universal relation $Z=0.71R_{fm}$, and for larger radii (measured in fm or km) $Z = 7 \times 10^{-5} R_{fm}^2 = 7 \times 10^{31} R_{km}^2$. For objects with nuclear density the relation corresponds to $Z \approx 0.7 A^{1/3}$ ($10^{8} < A < 10^{12}$) and $Z \approx 7\times10^{-5} A^{2/3}$ ($A > 10^{12}$), where $A$ is the baryon number. For some systems this universal upper bound improves existing charge limits in the literature.

Abstract:
A reply to arXiv:0809.2310, "Comment on Universal Charge-Radius Relation for Subatomic and Astrophysical Compact Objects" [arXiv:0804.2140,PRL100(2008)151102]

An
asymptotic method has been developed for investigation of kinetics of formation
of compact objects with strong internal bonds. The method is based on the
uncertainty relation for a coordinate and a momentum in space of sizes of
objects (clusters) with strongly pronounced collective quantum properties
resulted from exchange interactions of various physical nature determined by
spatial scales of the processes under consideration. The proposed
phenomenological approach has been developed by analogy with the all-known
ideas about coherent states of quantum mechanical oscillator systems for which
a product of coordinate and momentum uncertainties (dispersions) accepts the value,
which is minimally possible within uncertainty relations. With such an approach
the leading processes are oscillations of components that make up objects,
mainly: collective nucleon oscillations in a nucleus and phonon excitations in
a mesostructure crystal lattice. This allows us to consider formation and
growth of subatomic and mesoscopic objects in the context of a single
formalism. The proposed models adequately describe characteristics of formation
processes of nuclear matter clusters as well as mesoscopic crystals having
covalent and quasi-covalent bonds between atoms.

Abstract:
In this work we present preliminary results concerning the properties of about 50 clusters and associations located in a densely populated region at the Southern edge of the supershell LMC~4. The ages of the clusters and associations are derived. The cluster formation rate peaks at about 10-20 Myr ago corresponding to the age of the formation of LMC~4. Objects younger than 10 Myr are located close to CO clouds, indicating a possible trigger of the recent star formation by the interaction of the supershell with the interstellar medium. Isophotal analysis has been done for 50% of the clusters. A large number of objects present isophotal distortions commonly interpreted as sign of interaction. Cluster multiplets are coeval within 20 Myr, suggesting a common origin. This indicates that clusters possibly form in large groups. Our findings are in agreement with the unified view of multi-scale star formation, where a size-duration correlation is expected.

Abstract:
We study maximal $m$-rigid objects in the $m$-cluster category $\mathcal C_H^m$ associated with a finite dimensional hereditary algebra $H$ with $n$ nonisomorphic simple modules. We show that all maximal $m$-rigid objects in these categories have exactly $n$ nonisomorphic indecomposable summands, and that any almost complete $m$-rigid object in $\mathcal C_H^m$ has exactly $m+1$ nonisomorphic complements. We also show that the maximal $m$-rigid objects and the $m$-cluster tilting objects in these categories coincide, and that the class of finite dimensional algebras associated with maximal $m$-rigid objects is closed under certain factor algebras.

Abstract:
The causal interpretation of quantum mechanics is applied to the universe as a whole and the problem of cluster formation is studied in this framework. It is shown that the quantum effects be the source of the cluster formation.

Abstract:
In this note, we consider the $d$-cluster-tilted algebras, the endomorphism algebras of $d$-cluster-tilting objects in $d$-cluster categories. We show that a tilting module over such an algebra lifts to a $d$-cluster-tilting object in this $d$-cluster category.

Abstract:
We look at the program of modelling a subatomic particle---one having mass, charge, and angular momentum---as an interior solution joined to a classical general-relativistic Kerr-Newman exterior spacetime. We find that the assumption of stationarity upon which the validity of the Kerr-Newman exterior solution depends is in fact violated quantum mechanically for all known subatomic particles. We conclude that the appropriate stationary spacetime matched to any known subatomic particle is flat space.