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6c8c5b977ed51cdbc8e9d10a70ece85edb6534d0 | subsection | 9 | 14 | Kolmogorov-Smirnov test of the scaling function | Under the
significant level of 5%, the null hypothesis is rejected for six
stocks (000625, 600026, 600100, 600428, 600601, 600688) using the KS
test and for five stocks (000625, 600026, 600100, 600428, 600601)
using the KSW test. We find that the KS test and the KSW test
provide very similar results except that the KS ... | {
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"... | 10.1016/j.physa.2008.12.005 | 0807.1818 | Statistical properties of volatility return intervals of Chinese stocks | [
"Fei Ren",
"Liang Guo",
"Wei-Xing Zhou"
] | [
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a8c29b9c2a8c8843ee922422d9083eecad5923d8 | subsection | 10 | 14 | Memory effect of return intervals | The probability distribution may not fully characterize the
properties of volatility return intervals. The temporal correlation
is known as another important observable independent of the
probability distribution. Empirical studies have revealed that the
stock market volatilities are long-term correlated. We suppose th... | {
"cite_spans": []
} | 10.1016/j.physa.2008.12.005 | 0807.1818 | Statistical properties of volatility return intervals of Chinese stocks | [
"Fei Ren",
"Liang Guo",
"Wei-Xing Zhou"
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f5fc2ac8f8e6b49a4c3bc09c7456b108abcd6665 | subsection | 11 | 14 | Short-term memory of return intervals | To investigate the memory effect of the return intervals in Chinese
stock market, we first calculate the conditional probability
distribution P_q(\tau |\tau _0), which is the probability to find an
interval \tau immediately after the interval \tau _0.
Specifically, we study the conditional PDF for a bin of \tau _0.
The... | {
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} | 10.1016/j.physa.2008.12.005 | 0807.1818 | Statistical properties of volatility return intervals of Chinese stocks | [
"Fei Ren",
"Liang Guo",
"Wei-Xing Zhou"
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b70704454c0756612a6092f2a406cf48d13b9ae4 | subsection | 12 | 14 | Long-term memory of return intervals | To further study the long-term memory of return intervals, we
investigate the mean return interval \langle \tau | \tau _0 \rangle
after a cluster of n intervals that are all in a bin \tau _0. The
entire interval sequences are partitioned into two bins, separated
by the median value of return intervals. Thus we investi... | {
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1e02a45fcc2f7810a779e91e4f24c8dda77f3400 | subsection | 13 | 14 | Summary and conclusions | In summary, we have studied the distribution and memory effect of
volatility return intervals for 30 most actively traded stocks on
the Shanghai and Shenzhen Stock Exchanges. The Kolmogorov-Smirnov
tests are performed to examine the scaling behavior of the return
interval distributions as well as the particular form of... | {
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} | 10.1016/j.physa.2008.12.005 | 0807.1818 | Statistical properties of volatility return intervals of Chinese stocks | [
"Fei Ren",
"Liang Guo",
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a2e32122de25d019c5575bc4ab27fdf22e494318 | abstract | 0 | 14 | Abstract | An unsolved problem of classical mechanics and classical electrodynamics is
the search of the exact relativistic equations of motion for a classical
charged point-particle subject to the force produced by the action of its EM
self-field. The problem is related to the conjecture that for a classical
charged point-partic... | {
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} | 10.1063/1.3076465 | 0807.1819 | The exact radiation-reaction equation for a classical charged particle | [
"M. Tessarotto",
"M. Dorigo",
"C. Cremaschini",
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"A. Beklemishev"
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a1e00a23ce7eccb4bef2a42d2e5a405e886b96d6 | subsection | 1 | 14 | Introduction | A famous (and unsolved) theoretical issue both in classical and quantum
mechanics is related to the radiation reaction (RR) problem, i.e., the treatment of the dynamics of a charged particle in the
presence of its EM self-field (for an introduction and background see
Feyman, 1970 ) to be based on the construction of it... | {
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3f741a287f1e085b310b108feece7655d0d3b72b | subsection | 2 | 14 | Introduction | Another key
issue is, however, related to the condition of validity of the relativistic
Hamilton variational principle .In this paper we intend to analyze in detail a result which is already
well-known in the literature, namely that in its customary form the Hamilton
principle does not apply for point-particles. This i... | {
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ac6c8cd3bd5fb57765a193077a980dfafe4c488e | subsection | 3 | 14 | Variational description of classical point-particle relativistic
dynamics | From the mathematical viewpoint, one of the corner-stones of classical
mechanics is the assumption that the coupled set of equations formed by the
particle dynamical equations and Maxwell's equations is variational , . In other words, both the particle state and the EM field in
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3b1e14d01231ff07a37b10250ef85b8589c2afb0 | subsection | 4 | 14 | Variational description of classical point-particle relativistic
dynamics | In classical mechanics the
variational functional (the Hamilton action functional) is well-known, and
can be realized either by means of asynchronous or synchronous
variational principles. The variational functional (action
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e283ab21a0f3d23bcce751d5aac9db69e30d2347 | subsection | 5 | 14 | Variational description of classical point-particle relativistic
dynamics | It follows that : T_{1}) for arbitrary independent synchronous variations \delta f(s), the synchronous variational principle\delta S=0,delivers the following set of Euler-Lagrange equations for the
extremal curves f(s):&&\left. -d\left( m_{o}cu_{\mu }+\frac{q}{c}A_{\mu }\right) +\frac{q}{c}\frac{\partial }{\partial r^{... | {
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d1e16850f371fd72c4b4dfa2b1d3a97cb6cb3aae | subsection | 6 | 14 | Variational description of classical point-particle relativistic
dynamics | To
obtain the Euler-Lagrange equation for \delta A_{\mu } one invokes the
identities\frac{1}{16\pi }\delta \int \frac{d\Omega }{\sqrt{-g}}F^{\mu \nu }F_{\mu \nu }=-\frac{1}{4\pi }\int \frac{d\Omega }{\sqrt{-g}}\delta A_{\nu }\partial _{\mu }F^{\mu \nu },\delta \int _{s_{1}}^{s_{2}}dsA_{\mu }(r(s))\frac{dr^{\mu }(s)}{ds... | {
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7e5a00de0c6dae2e2c2757a0e3a92bc0795cf7ae | subsection | 7 | 14 | Variational description of classical point-particle relativistic
dynamics | In such a case the following result can be proven:THM.2 - Violation of THM.1 for the EM self-force of point-particlesAs a consequence of THM.1 it follows that: C_{1}) the
Euler-Lagrange equations obtained by imposing an arbitrary synchronous
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b0812c18b66b4537e7af5f5a104340dbd8e4e3a5 | subsection | 8 | 14 | Variational description for finite-size charges | THM.2 implies the fundamental consequence that for point-particles the
variational principle (REF ) becomes invalid if the
EM 4-potential A_{\mu }^{(self)} is properly taken into account. This is
due to the divergences produced by the self-force generated by the point
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43674feab2eef3f7abddbd0be76e1425471c7619 | subsection | 9 | 14 | Variational description for finite-size charges | \\
&&+\frac{1}{16\pi c}\int \frac{d\Omega }{\sqrt{-g}}F^{\mu \nu }F_{\mu \nu }+\int _{s_{1}}^{s_{2}}\frac{d\Omega }{\sqrt{-g}}W(r,s)\chi (s)\left[ u_{\mu }(s)u^{\mu }(s)-1\right] ,while - similarly - the 4-current j^{\mu }(r^{\nu }) reads j^{\mu }(r^{\nu })=qc\int \frac{d\Omega ^{\prime }}{\sqrt{-g}}W(r^{\prime },s^{\p... | {
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1aab4558b9516555423b482bcbfb5aefb22dd41d | subsection | 10 | 14 | Variational description for finite-size charges | S(r^{\mu },u_{\mu },\chi ,A_{\mu })=\frac{1}{4\pi }\int _{s_{1}}^{s_{2}}ds\int d\Sigma (\mathbf {n})\left( m_{o}cu_{\mu }(\mathbf {n,}\text{ }s)+\frac{q}{c}A_{\mu }(r(\mathbf {n,}\text{ }s))\right) \frac{dr^{\mu }(\mathbf {n,}\text{ }s)}{ds}+\right. \\
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376c3859ced2b5fe50d4abe2bc888f9ed4375ed4 | subsection | 11 | 14 | Variational description for finite-size charges | In
particular, the Euler-Lagrange equations for \delta A_{\mu }(\mathbf {n,}s)
- again to be identified with Maxwell's equations - follow by noting that
the functional \int ds\int d\Sigma (\mathbf {n})A_{\mu }(r(s))\frac{dr^{\mu }(\mathbf {n,}\text{ }s)}{ds} can also be written as \int ds^{\prime }\int \frac{d\Omega ^{... | {
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12e3621ac14c526ab6dd9b804af1086c5cebc064 | subsection | 12 | 14 | Conclusions | In this paper the variational treatment of the radiation-reaction problem
has been investigated. First we have analyzed the Hamilton variational
principle, proving that it becomes invalid for charged point-particles if
the proper form of the EM self-field prescribed by classical electrodynamics
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2cff23f9ffedf510c722b344b1e8f9ee44ce68ab | subsection | 13 | 14 | Notice | ^{§} contributed paper at RGD26 (Kyoto, Japan, July 2008). | {
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701c9cf47e29b018b41c8f91f0c3f5e3933ece7a | abstract | 0 | 19 | Abstract | Some ingredients of the BRST construction for quantum Lie algebras are
applied to a wider class of quadratic algebras of constraints. We build the
BRST charge for a quantum Lie algebra with three generators and
ghost-anti-ghosts commuting with constraints. We consider a one-parametric
family of quadratic algebras with ... | {
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20ea516636121179c84c6e87c7807716ad9905b1 | subsection | 1 | 19 | Introduction | The construction of BRST charges Q for linear (Lie) algebras of constraints is well known. In the case of nonlinear
algebras, despite the existence of quite general results concerning the structure of the BRST charges (see, e.g.,
, , and references therein), the general construction is far from being fully understood.
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34522c2654bc1b7c86b1c97b0f934d7c5b49ed54 | subsection | 2 | 19 | Quantum space formalism | Let V_{N+1} be an (N+1)-dimensional vector space. | {
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eedf2554a59f984dc8e13fbfb374895a43cfc324 | subsection | 3 | 19 | Quantum space formalism | Let R\in {\rm End}(V_{N+1}\otimes V_{N+1})
be a Yang-Baxter R-matrix, that is, a solution of the Yang-Baxter equationR_{\underline{2} \underline{3}}\, R_{\underline{1}\underline{2}}\,
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6c0b1cd45f169fcbb10414497b3cbdb0d48bb01d | subsection | 4 | 19 | Quantum space formalism | Indeed, using
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81f4a6a83704ede038ec64de4b53c3bba7edf17c | subsection | 5 | 19 | Quantum space formalism | The compatibility of c^0 (REF ) with
(REF ), (REF ) and (REF ) yields the unique solution for tensors
X_{i_{1}\dots i_{k+1}}^{j_{1}\dots j_{k}} in terms of the matrix components F^{CD}_{AB} and
R^{CD}_{AB}. In papers , we analyzed the case F=R
with a particular R-matrix (see eq.(REF ) below) and found in this case the ... | {
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7b692fae925ee2bd2d309e55a8da72b3ad91249b | subsection | 6 | 19 | BRST operator for finitely generated quadratic algebras | Consider a (N+1)^2\times (N+1)^2 Yang-Baxter matrix with the following restrictions on the
components R^{CD}_{AB} :R^{ij}_{kl}=\sigma ^{ij}_{kl}\; ,\;\;\; R^{0j}_{kl}=C^{j}_{kl}\; ,\;\;\; R^{0A}_{B0}=R^{A0}_{0B}=\delta ^A_B\;(other components of R vanish). Small letters i,j,k,\dots =1,\dots ,N denote indices of the
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f9bbfe2b3a021d58378b4271fbb8365a38d243f5 | subsection | 7 | 19 | BRST operator for finitely generated quadratic algebras | The rescaled generators (still denoted by \chi _i, i =1,2,\dots ,N) satisfy relations\chi _{i_1}\,\chi _{i_2}-\sigma ^{k_1 k_2}_{i_1 i_2}\,\chi _{k_1}\,\chi _{k_2}=
C^{k_1}_{i_1i_2}\,\chi _{k_1} \qquad {\mathrm {or}}\qquad \chi _{1\rangle }\,\chi _{2\rangle }-\sigma _{12}
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a4f3748cf9b0e51195c162b5c275b9b3dc5917a8 | subsection | 8 | 19 | BRST operator for finitely generated quadratic algebras | The usual Lie
algebras form a subclass of the QLA corresponding to \sigma ^{ij}_{km} = \delta ^i_m \delta ^j_k
(i.e., \sigma is the permutation).Below we consider the simplest, unitary, braid matrices \sigma , that is,\sigma _{nm}^{pj}\sigma ^{ki}_{pj}=\delta ^k_n\delta ^i_m\qquad {\mathrm {or}}\qquad \sigma ^2 = 1\; .... | {
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cb15d3098e195fb963b8e3c01985311953d35fdc | subsection | 9 | 19 | BRST operator for finitely generated quadratic algebras | For consistency of the algebra \Omega we
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\; , \;\;\phi _{12}\,\phi _{23}\,\sigma _{12}=\sigma _{23}\,\phi _{12}\,\phi _{23}\; ,\\[1em]
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809c049245c0f641376661ff2f540ec716889230 | subsection | 10 | 19 | Example of a 3-dimensional QLA | In this Section we present an explicit example of a finite-dimensional QLA
(REF )–(REF ) and construct the BRST charge for this algebra.The algebra we start with has four generators \lbrace \chi _0,\chi _1,\chi _2,\chi _3\rbrace which obey the
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f4e16c8709659a299aa564285526011997395454 | subsection | 11 | 19 | Example of a 3-dimensional QLA | \end{array}The matrix \sigma has the form \sigma _{12}=P_{12}+u_{12}, where u_{12}=-u_{21} and
u_{12}^2=0, so \sigma ^2=1 (\sigma belongs to the family F in the classification of GL(3)
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dee3677fac3b32a1f455906c1bdb86bbca0a4c16 | subsection | 12 | 19 | Example of a 3-dimensional QLA | Then the BRST operator (REF ) for the
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85f4ed529f94d8c7d274548e7f8e946e3c654461 | subsection | 13 | 19 | BRST operator for a 3-dimensional nonlinear algebra | We construct the BRST operator for the algebra, which generalizes the QLAs (REF ) and (REF ):[J,\, W]=a_1T+a_2J^2\; ,\;\;\; [J,\, T]=0 \; ,\;\;\; [T,\, W]=a_3J\, T\; ,with a_1,a_2,a_3\ne 0. By rescaling of the generators, two of three coefficients \lbrace a_1,a_2\rbrace
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4353e76ced5a1e8a54bf79feb065a0b9044f510d | subsection | 14 | 19 | BRST operator for a 3-dimensional nonlinear algebra | If we relax the
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e82617472b0a08892caf484d4422b63778bcb863 | subsection | 15 | 19 | BRST operator for a 3-dimensional nonlinear algebra | To relate this ghost-anti-ghost algebra and the BRST charge
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71666b05a03245a4f0937309f2e12d08a9beb973 | subsection | 16 | 19 | Double BRST complex | An interesting peculiarity of the family (REF ) of non-linear algebras is an existence
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db14e93250595c786b5165930dd72d6822d65a19 | subsection | 17 | 19 | Double BRST complex | For an algebra, having several quadratic faces, related by nonlinear transformations, one can
impose standard initial condition in any of them and build – in general nonequivalent – BRST
charges (cf. the Lie algebra [x,y]=y and transformations x\mapsto x+f(y), f is a
polynomial). | {
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} | 10.1134/S1547477110040011 | 0807.1820 | BRST charges for finite nonlinear algebras | [
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2804ad8556ed3ded7b432d8ddc127f9b648d1ad5 | subsection | 18 | 19 | Conclusion | We extended some elements of the construction of BRST charge for quantum Lie algebras to more
general quadratic algebras. We explicitly found the BRST charges in the examples when the
constraints commute with the ghost-anti-ghosts. We discussed an example of a QLA with three
generators and presented the BRST charge for... | {
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} | 10.1134/S1547477110040011 | 0807.1820 | BRST charges for finite nonlinear algebras | [
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646c53a5f12eec4b284ea35054eafc5d6befb07d | abstract | 0 | 12 | Abstract | Recently a simple proof of the generalizations of Hawking's black hole
topology theorem and its application to topological black holes for higher
dimensional ($n\geq 4$) spacetimes was given \cite{rnew}. By applying the
associated new line of argument it is proven here that strictly stable
untrapped surfaces do possess... | {
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} | 10.1088/0264-9381/26/5/055017 | 0807.1821 | On the topology of untrapped surfaces | [
"István Rácz"
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0d2f7c5c245a641dcf2921b96cf82c4b45f12c6d | subsection | 1 | 12 | Introduction | Hawking's black hole topology theorem plays a key role in
4-dimensional black hole physics from the beginning of the 70's. By making
use of a variant of Hawking's argument, almost three decades later, in the
late 90's, Gibbons and Woolgar could also characterize
the so-called “topological black hole” spacetimes—to whic... | {
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9fbe2c02c7f6960a7f57999122c1baa59182b8e0 | subsection | 2 | 12 | Preliminaries | Since our argument does apply to any metric theory of gravity within this
paper, likewise in , a spacetime is supposed to be represented by a
pair (M,g_{ab}), where M is an n-dimensional (n\ge 4), smooth,
paracompact, connected, orientable manifold while g_{ab} is a smooth
Lorentzian metric of signature (-,+,\dots ,+) ... | {
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cebefb2f59dce7aa38f628107b44f8143b74e11a | subsection | 3 | 12 | Preliminaries | Then the null
expansions \theta ^{(\ell )} and \theta ^{(n)} with respect to \ell ^a and
n^a are defined as£_\ell \,{\epsilon }{\hspace{-3.98032pt}\epsilon }_q=\theta ^{(\ell )}\,{{\epsilon }{\hspace{-3.98032pt}\epsilon }}_q
{ \ \ {\rm and}\ \ }
£_n\,{{\epsilon }{\hspace{-3.98032pt}\epsilon }}_q= \theta ^{(n)}\,{{\epsi... | {
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dad0a5c9cd9ba5d2503b57039e38855c01419def | subsection | 4 | 12 | Preliminaries | It is straightforward to see that for any particular choice
of A and B the vector field Z^a is smooth and spacelike everywhere on
{S} whenever A and B are both positive or negative throughout
{S}.In order to justify that a meaningful quasi-local concept of outwards and
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05fd902ab45429ae36384b4767ac830cf54e1f41 | subsection | 5 | 12 | Preliminaries | It is worth emphasizing, however, that the
signs of \theta ^{(\ell )} and \theta ^{(n)}, and, in turn, the notion of
trapped, untrapped and marginal surfaces, along with the above defined
quasi-local notion of outwards and inwards directions, are intact under such a
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2deb3b92f5086788703203d2c5f17d491822e17e | subsection | 6 | 12 | Preliminaries | The Yamabe invariant
\mathcal {Y}({S}) is defined then as the supremum of the Yamabe
constants associated with {S}, i.e., \mathcal {Y}({S}) =
\sup _{[q]}Y({S},[q]).It is worth recalling that according to important results of Aubin and Schoen
the Yamabe invariant \mathcal {Y}({S}) is known to be bounded
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ab0c82495e0969c5c30c53a70f750df35f7107f4 | subsection | 7 | 12 | The main result | Now, by making use of the above recalled notions, our main result is
formulated as.Theorem 3.1 Let (M,g_{ab}) be a spacetime of dimension
n\ge 4 in a metric theory of gravity. Assume that the generalized dominant
energy condition, with smooth real function f:M\rightarrow \mathbb {R}, holds
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04bd30d5ac26a3772f7a77bd86c19c2aff53b823 | subsection | 8 | 12 | The main result | The elementary spacetime neighborhood \mathcal {O} is smoothly
foliated then by the 2-parameter family of (n-2)-dimensional u=const,
r=const level surfaces {S}_{u,r}, furthermore, the spacetime
metric in \mathcal {O} takes the formg_{ab}=2\,\left(\nabla _{(a}r - r\,\alpha \,\nabla _{(a}u - r\,\beta _{(a}\right)
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619a5eec023d074f79a847be6916e46d09fcc6ec | subsection | 9 | 12 | The main result | Finally, recall
that {S} was assumed to be a strictly stable untrapped surface which
ensures that the null normals n^a and \ell ^a may be assumed, without loss
of generality, to be such that
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ecdafeb64c2278c28871a1051777d62c145a8808 | subsection | 10 | 12 | Discussion | Let us return now to the interpretation of the stability condition we have
applied. To this end note first that the second variation
\delta _n\delta _\ell \mathcal {A}=\frac{{\rm \partial ^2}
\mathcal {A}({S}_{u,r})}{ \partial u\,\partial r}\vert _{u=0,r=0} of
the area in the principal null
directions \ell ^a and n^a r... | {
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... | 10.1088/0264-9381/26/5/055017 | 0807.1821 | On the topology of untrapped surfaces | [
"István Rácz"
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64d165837853b3ff047d8454c32a7a97d1cdd3b9 | subsection | 11 | 12 | Discussion | Introducing then the notation \psi =e^{-2v} and
s_a=\frac{1}{2}\beta _a, it can be verified (see also for more
details) that (REF ) takes the form&&\hspace{-14.22636pt}\big (\big [£_{
n^{\prime }}\theta ^{(\ell ^{\prime })}+\theta ^{(\ell ^{\prime })}\,\theta ^{( n^{\prime })}\big ]\,\psi \big )
\vert _{{S}}=
-D^aD_a\p... | {
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901a1c305df51397f4f4976656fa9bdaf01eb5b7 | abstract | 0 | 28 | Abstract | We discuss the open charm production in peripheral reactions
$\bar pp\to \bar Y_cY_c$ and $\bar pp\to M_c\bar M_c$, where
$Y_c$ and $M_c$ stand for $\Lambda_c^+,\Sigma_c^+$ and
$D,D^*$, respectively, at $\sqrt{s}\lesssim 15$ GeV, which corresponds to the
energy range of FAIR. Our consideration is based on the topolo... | {
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} | 10.1103/PhysRevC.78.025201 | 0807.1822 | Exclusive charm production in pbar p collisions at s^1/2 <15 GeV | [
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"B. Kampfer"
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f2b22c6a7eb12f33081c508ec04c6d88f9907bc5 | subsection | 1 | 28 | Introduction | Open charm production will be one of the major topics of the
hadron and heavy-ion programme at FAIR .
On the one hand, charm spectroscopy will be addressed by
the PANDA collaboration , while the CBM collaboration
will exploit
charmed particles as probes of the nuclear medium at maximum compression.
For both large-scal... | {
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... | 10.1103/PhysRevC.78.025201 | 0807.1822 | Exclusive charm production in pbar p collisions at s^1/2 <15 GeV | [
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f3c6c4953821515cfa831da0b85cf965fe7f3e3e | subsection | 2 | 28 | Introduction | The binary
\pi ^-p\rightarrow D^-\Lambda _c exclusive process plays an important role
in this consideration . The model for this
reaction is based on quark-gluon string dynamics, assuming the
annihilation of a q\bar{q} pair in the interaction, the formation of a
q\bar{q} color tube with subsequent decay to the observed... | {
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084bb71eb60f7f848ea7ffec3ce98b61ed973134 | subsection | 3 | 28 | Introduction | II we analyze
the strangeness production in the reactions
\bar{p}p\rightarrow \bar{\Lambda }\Lambda , \bar{p}p\rightarrow \bar{\Lambda }\Sigma ^0,
and \bar{p}p\rightarrow \bar{\Sigma }^0\Sigma ^0, and the open charm production in
\bar{p}p\rightarrow \bar{\Lambda }^+_c\Lambda ^+_c,
\bar{p}p\rightarrow \bar{\Lambda }^+_c... | {
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} | 10.1103/PhysRevC.78.025201 | 0807.1822 | Exclusive charm production in pbar p collisions at s^1/2 <15 GeV | [
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8b043bf0acb2ab7169e9eff1bba0b219b14db2d9 | subsection | 4 | 28 | Reactions | In this section, we discuss strange and charmed baryon-antibaryon
production in peripheral \bar{p}p collisions. For the sake of simplicity, we
consider the exclusive production of \bar{\Lambda }\Lambda and
\bar{\Lambda }_c\Lambda _c pairs. The generalization for reactions with
\bar{\Lambda }\Sigma , \bar{\Sigma }\Lambd... | {
"cite_spans": []
} | 10.1103/PhysRevC.78.025201 | 0807.1822 | Exclusive charm production in pbar p collisions at s^1/2 <15 GeV | [
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cc5a209fd246841b3fbfeff3c18c119172b85777 | subsection | 5 | 28 | Reaction | Following Ref. we assume that the
amplitude of the reaction \bar{p}p\rightarrow \bar{\Lambda }\Lambda has the
form of a Regge pole amplitude, dominated by the K^* exchange
trajectory,T^{\bar{p}p\rightarrow \bar{\Lambda }\Lambda }_{m_f n_f;m_i,n_i}
=C(t){\cal M}^{\bar{p}p\rightarrow \bar{\Lambda }\Lambda }_{m_f n_f;m_i... | {
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c656df2076675b51ada1a2e8f87ad1afe4a79e17 | subsection | 6 | 28 | Reaction | In the diffractive
region with -t\ll T, the linear approximation\alpha (t)=\alpha (0)+\alpha ^{\prime }t,is valid with \alpha ^{\prime }=\gamma /2\sqrt{T}.The intercept \alpha _{\bar{s}q}(0) and the slope \alpha _{\bar{s}q}^{\prime } of the trajectory for the non-diagonal transition are
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f587482aa94c7926edc757a4481d0a44cb0a7cb7 | subsection | 7 | 28 | Reaction | (REF ) is related to the corresponding scale parameters
for the diagonal transitions \bar{p}p\rightarrow \bar{p}p, (s_{\bar{p}p} ) and \bar{\Lambda }\Lambda \rightarrow \bar{\Lambda }\Lambda , (s_{\bar{\Lambda }\Lambda }) as\left(s_{\bar{p}p:\bar{\Lambda }\Lambda }\right)^{2(\alpha _{K^*}(0)-1)} = \left(s_{\bar{p}p}\ri... | {
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6db00bb8c58a93bbd49a0e4f481bfc8d841ebe47 | subsection | 8 | 28 | Reaction | (REF ) as{\cal M}^{\bar{p}p\rightarrow \bar{\Lambda }\Lambda }_{m_f n_f;m_i n_f}(s,t)
&=&{\cal N}(s,t)\,\Gamma ^{(p)\,\mu }_{m_fm_i}\,\,
\Gamma ^{(\bar{p})\,\nu }_{n_f n_i}\,\,
(-g_{\mu \nu } + \frac{q_\mu q_\nu }{q^2})~,where q is momentum transfers in the p\Lambda K^* vertex:
q=p_p-p_\Lambda , with p_p and p_\Lambda ... | {
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0cb5d25872fb7a5b4758b3888c5f95401ab6c03e | subsection | 9 | 28 | Reaction | (REF ) which is beyond the Regge parametrization:{\cal N}(s,t)&=&
\frac{F_{\infty }(s)}{F(s,t)},\qquad F_{\infty }(s)=2s~, \\
F^2(s,t)&=& {\rm Tr}
\left(\Gamma ^{(p)\,\mu }{\Gamma ^{(p)\,\mu ^{\prime }}}^\dagger \right) {\rm Tr}\left(\Gamma ^{(\bar{p})\,\nu } {\Gamma ^{(\bar{p})\,\nu ^{\prime }}}^\dagger \right)\, (g_{... | {
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]
} | 10.1103/PhysRevC.78.025201 | 0807.1822 | Exclusive charm production in pbar p collisions at s^1/2 <15 GeV | [
"A. I. Titov",
"B. Kampfer"
] | [
"hep-ph"
] | 2,008 | en | Physics | [
15,
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e16fb7faee4997b8d20ed994d339123b7cdfe55d | subsection | 10 | 28 | Reaction | As a first approximation, we
assume the validity of SU(4) symmetry and, therefore, the coupling
constants of the D^{*}NY_c interaction are chosen to be the same
as for the case of K^*NY interaction. The corresponding
trajectory and the energy scale parameters read\alpha _{D^*}(0)&=& -1.02,\qquad \sqrt{T_{D^*}}=3.91~{\r... | {
"cite_spans": []
} | 10.1103/PhysRevC.78.025201 | 0807.1822 | Exclusive charm production in pbar p collisions at s^1/2 <15 GeV | [
"A. I. Titov",
"B. Kampfer"
] | [
"hep-ph"
] | 2,008 | en | Physics | [
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97a7e46d58ecef278ca0286b074f1a8b2ea8c84d | subsection | 11 | 28 | Reaction | The overall residual function C^{\prime }(t)
will be found again from a comparison with available experimental
data.The parameters of the trajectory for the non-diagonal transition
\alpha _{ ds} are related to the corresponding parameters for the
"diagonal" transitions \alpha _{\bar{s}s} and \alpha _{\bar{d}d}
similarl... | {
"cite_spans": [
{
"arxiv_id": "",
"doi": "",
"end": 822,
"openalex_id": "",
"raw": "J. K. Storrow, Phys. Rept. 103, 317 (1984).",
"source_ref_id": "5a3eaab06389ef47d3ffae9ceceead96a4be2d6f",
"start": 514
}
]
} | 10.1103/PhysRevC.78.025201 | 0807.1822 | Exclusive charm production in pbar p collisions at s^1/2 <15 GeV | [
"A. I. Titov",
"B. Kampfer"
] | [
"hep-ph"
] | 2,008 | en | Physics | [
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234c7522463491332737ff4550724b963bc211d7 | subsection | 12 | 28 | Reaction | (REF )&&{\cal M}^{\bar{p}p\rightarrow \bar{K}K}_{m_i n_i}(s,t)= {\cal N}(s,t)\,\left[\bar{v}_{n_i}\,
(p\!\!\!/_Y - M_Y )\, u_{m_i}\right]~,\\
&& {\cal N}(s,t)=
\frac{F_{\infty }(s)}{F(s,t)},\qquad F^2_{\infty }(s)=s\,M_Y^2/2~,
\\
&&F^2(s,t) =\frac{1}{2}\,\left( (s-2M_N^2)(M_Y^2-t)
+4M_NM_Y(M_N^2+M_K^2+t \right.
\\
&&\l... | {
"cite_spans": [
{
"arxiv_id": "",
"doi": "",
"end": 533,
"openalex_id": "",
"raw": "V. G. J. Stoks and T. A. Rijken, Phys. Rev. C 59, 3009 (1999).",
"source_ref_id": "af2016ce4e4bde04d3630f7ed5ae2d05aeb5b7b9",
"start": 389
},
{
"arxiv_id": "",
"doi":... | 10.1103/PhysRevC.78.025201 | 0807.1822 | Exclusive charm production in pbar p collisions at s^1/2 <15 GeV | [
"A. I. Titov",
"B. Kampfer"
] | [
"hep-ph"
] | 2,008 | en | Physics | [
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73cd8a7c963fa0fcc7c1541154c420f6af1b3975 | subsection | 13 | 28 | Reaction | The
\Lambda _c trajectory is calculated using2\alpha _{ dc}(0)&=&\alpha _{\bar{d}d}(0)+\alpha _{\bar{c}c}(0)~,
\\
{2}/{\alpha ^{\prime }_{ dc}}&=& {1}/{\alpha _{\bar{d}d}^{\prime }}+{1}/{ \alpha _{\bar{c}c}^{\prime }}~,where \alpha _{\bar{c}c}(t)\equiv \alpha _{J/\psi }(t) and \alpha _{
dd}(t) are defined by Eqs. (REF ... | {
"cite_spans": []
} | 10.1103/PhysRevC.78.025201 | 0807.1822 | Exclusive charm production in pbar p collisions at s^1/2 <15 GeV | [
"A. I. Titov",
"B. Kampfer"
] | [
"hep-ph"
] | 2,008 | en | Physics | [
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817c991817aa6a14b6b183244eed68cc5d52ce15 | subsection | 14 | 28 | Reaction | III, s_{\bar{p}p:\bar{K}K^*}=s_{\bar{p}p:\bar{K}K}, and
C^{\prime }(t) is defined in Eq. (REF )The spin dependent amplitude {\cal M} has the following form{\cal M}^{\bar{p}p\rightarrow \bar{K}K}_{\lambda _f;m_i n_i}(s,t) = {\cal N}(s,t)\,\Gamma ^{\mu }_{\lambda _f;m_in_i}with\Gamma ^{\mu }_{\lambda _f;m_in_i}
=\bar{v}_... | {
"cite_spans": []
} | 10.1103/PhysRevC.78.025201 | 0807.1822 | Exclusive charm production in pbar p collisions at s^1/2 <15 GeV | [
"A. I. Titov",
"B. Kampfer"
] | [
"hep-ph"
] | 2,008 | en | Physics | [
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b4c339c5e6f1b0d4e7970c27ad80bbf77fe2799d | subsection | 15 | 28 | Reaction | In the case of \bar{K}^0K^{*0}, the amplitude is defined by the
\Sigma ^+ exchange trajectory.The amplitude for the \bar{K}^*K reaction has a similar form:\Gamma ^{\mu }_{\lambda _f;m_in_i}
=\bar{v}_{n_i}\,\left[
(\gamma ^\mu + \frac{\kappa _{NYK^*}}{ 2(M_N+M_Y) }(\gamma ^\mu p\!\!\!/_{K^*}
- p\!\!\!/_{K^* }\gamma ^\mu... | {
"cite_spans": []
} | 10.1103/PhysRevC.78.025201 | 0807.1822 | Exclusive charm production in pbar p collisions at s^1/2 <15 GeV | [
"A. I. Titov",
"B. Kampfer"
] | [
"hep-ph"
] | 2,008 | en | Physics | [
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4d3021446aed2db7b0021737b2471e96b37a361a | subsection | 16 | 28 | Reaction | The ratio of the cross sections with
D^-D^{*+} and \bar{D}^0D^{^0} final states is defined by the
coupling constants in KN\Sigma ,\,{K^*N\Sigma } and
{KN\Lambda },\,{K^*N\Lambda } interactions and is close to 0.03.
The cross sections decrease with energy similarly to the \bar{p}p\rightarrow D\bar{D} reactions, and ther... | {
"cite_spans": []
} | 10.1103/PhysRevC.78.025201 | 0807.1822 | Exclusive charm production in pbar p collisions at s^1/2 <15 GeV | [
"A. I. Titov",
"B. Kampfer"
] | [
"hep-ph"
] | 2,008 | en | Physics | [
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306b15470fa8975107c6b6dd27e9dcf0c9f21d62 | subsection | 17 | 28 | Reaction | One can see
an increase of the asymmetry with -t and its almost constant value
at large \sqrt{s} and fixed t_{\rm max}-t. The difference in
{\cal A} for \bar{K}^0K^{*0} and K^+K^{*-} final states is
mainly due to the difference in tensor couplings in
{K^*N\Sigma } and {K^*N\Lambda } interactions. For completeness,
we a... | {
"cite_spans": []
} | 10.1103/PhysRevC.78.025201 | 0807.1822 | Exclusive charm production in pbar p collisions at s^1/2 <15 GeV | [
"A. I. Titov",
"B. Kampfer"
] | [
"hep-ph"
] | 2,008 | en | Physics | [
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3ce2cd6aebececa43681b55eea9f03cfa9335b45 | subsection | 18 | 28 | Differential cross sections | Consider first the strange hyperon production \bar{p}p\rightarrow \bar{Y}Y
which we use to fix the residual factor C(t) in Eq. (REF ).
In Fig. REF we show the differential cross section
of the reaction \bar{p}p\rightarrow \bar{\Lambda }\Lambda and
\bar{p}p\rightarrow \bar{\Lambda }\Sigma ^0
as a function of the momentu... | {
"cite_spans": [
{
"arxiv_id": "",
"doi": "",
"end": 430,
"openalex_id": "",
"raw": "H. Becker et al. [CERN-Munich Collaboration], Nucl. Phys. B 141, 48 (1978).",
"source_ref_id": "369542bab2e781400730777c7d9f81a1a5e85253",
"start": 135
}
]
} | 10.1103/PhysRevC.78.025201 | 0807.1822 | Exclusive charm production in pbar p collisions at s^1/2 <15 GeV | [
"A. I. Titov",
"B. Kampfer"
] | [
"hep-ph"
] | 2,008 | en | Physics | [
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5cfe692cc6f38a800f6487d9d16724514d3b9acc | subsection | 19 | 28 | Differential cross sections | The ratio of the cross sections
with \bar{\Lambda }\Lambda , \bar{\Lambda }\Sigma ^0 and
\bar{\Sigma }^0\Sigma ^0 final states at large energy reads1 : r :r^2,where r=(g_{K^*N\Lambda }/g_{K^*N\Sigma })^{-2}\simeq 0.4.
[Figure: Left panel:The differential cross sections of the reactions\bar{p} p\rightarrow \bar{\Lambda ... | {
"cite_spans": []
} | 10.1103/PhysRevC.78.025201 | 0807.1822 | Exclusive charm production in pbar p collisions at s^1/2 <15 GeV | [
"A. I. Titov",
"B. Kampfer"
] | [
"hep-ph"
] | 2,008 | en | Physics | [
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af61046e5e6525ca004b8909e1d25b792158650a | subsection | 20 | 28 | Differential cross sections | REF .
[Figure: Differential cross section of the \bar{p} p\rightarrow K^-K^+reaction as a function of momentum transfer t at p_L=5 GeV.The contributions from \Lambda and \Sigma exchanges are shownby dashed and dot dashed curves, respectively.The experimental data are taken from Ref. .]The separate contributions from \L... | {
"cite_spans": []
} | 10.1103/PhysRevC.78.025201 | 0807.1822 | Exclusive charm production in pbar p collisions at s^1/2 <15 GeV | [
"A. I. Titov",
"B. Kampfer"
] | [
"hep-ph"
] | 2,008 | en | Physics | [
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113226151880b07b5a573ffef0380882ecf63d92 | subsection | 21 | 28 | Differential cross sections | The ratio of the cross
sections with D^-D^+ and \bar{D}^0D^0 final states
is close to
(\sqrt{2}\,g_{KN\Sigma }/g_{KN\Lambda })^4\simeq 0.034.
The cross sections decrease rapidly with energy as s^{-6.18},
therefore, the region with small excess energy is more
suitable for studying these reactions. | {
"cite_spans": []
} | 10.1103/PhysRevC.78.025201 | 0807.1822 | Exclusive charm production in pbar p collisions at s^1/2 <15 GeV | [
"A. I. Titov",
"B. Kampfer"
] | [
"hep-ph"
] | 2,008 | en | Physics | [
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0.1937255859375,
0.187... |
91a55145230a8790072d41e3e5947f044a09a74c | subsection | 22 | 28 | Longitudinal asymmetries | For a better understanding of the results of our numerical calculation, it
seems to be useful to perform a qualitative analysis of the
longitudinal asymmetry at forward production angle
(or t=t_{\rm max}), where the orbital interaction is absent. In this case, the
amplitude of the \bar{p}p\rightarrow \bar{Y}Y reaction ... | {
"cite_spans": []
} | 10.1103/PhysRevC.78.025201 | 0807.1822 | Exclusive charm production in pbar p collisions at s^1/2 <15 GeV | [
"A. I. Titov",
"B. Kampfer"
] | [
"hep-ph"
] | 2,008 | en | Physics | [
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c0a9810fa4a7cae90e70173aae584579fd9a4dda | subsection | 23 | 28 | Longitudinal asymmetries | The left and right panels correspond tothe reactions \bar{p} p\rightarrow \bar{\Lambda }\Lambda and \bar{p} p\rightarrow \bar{\Lambda }_c\Lambda _c, respectively.]In the case when M_p\simeq M_Y or/and at high energies,
when \sqrt{s}\gg M_Y, a_\kappa \rightarrow 0
and the spin-conserving amplitude becomes independent of... | {
"cite_spans": []
} | 10.1103/PhysRevC.78.025201 | 0807.1822 | Exclusive charm production in pbar p collisions at s^1/2 <15 GeV | [
"A. I. Titov",
"B. Kampfer"
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6b2559cb5ee6147090e6d8903bc6b5cf8fbaf376 | subsection | 24 | 28 | Longitudinal asymmetries | REF (right panel), and results in a large value of the
longitudinal asymmetry.For the \bar{p}p\rightarrow \bar{\Lambda }\Sigma \,(\bar{\Sigma }\Sigma )
reactions the spin-flip amplitude |B(s)| is small because of
the small magnetic strength, 1+\kappa \simeq 0.09, and the
asymmetry is almost zero.
[Figure: Left panel:Th... | {
"cite_spans": []
} | 10.1103/PhysRevC.78.025201 | 0807.1822 | Exclusive charm production in pbar p collisions at s^1/2 <15 GeV | [
"A. I. Titov",
"B. Kampfer"
] | [
"hep-ph"
] | 2,008 | en | Physics | [
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ae9a530170a5b717b0f71bb0419b3af5dc588811 | subsection | 25 | 28 | Reaction | In this section, we discuss the production of \bar{M}M
(with \bar{M}M being \bar{K}K or D\bar{D})
in \bar{p}p collisions. We assume that at small momentum transfer -t,
where
t=(p_p-p_K)^2 or t=(p_p-p_{\bar{D}})^2, the dominant contribution comes
from the baryon exchange channels.As an example, in Fig. REF (a) and (b) w... | {
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... | 10.1103/PhysRevC.78.025201 | 0807.1822 | Exclusive charm production in pbar p collisions at s^1/2 <15 GeV | [
"A. I. Titov",
"B. Kampfer"
] | [
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0cea667c2b500dc0e71f0917e929b69c0830b1af | subsection | 26 | 28 | Longitudinal asymmetry | In reactions \bar{p}p\rightarrow \bar{K}K (D\bar{D}) at forward production
angle (or t=t_{\rm max}), the spin in the final state is equal
to zero. This means that the production amplitude may be expressed
asT_{m_i,n_i}\sim B(s)\,\delta _{m_i-n_i}~,and therefore, the asymmetry in Eq. (REF ) {\cal A}=1. At
finite angles,... | {
"cite_spans": []
} | 10.1103/PhysRevC.78.025201 | 0807.1822 | Exclusive charm production in pbar p collisions at s^1/2 <15 GeV | [
"A. I. Titov",
"B. Kampfer"
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bde643d5fddc078ee61d21ebb4c1fd166fa0b832 | subsection | 27 | 28 | Summary | In summary, we have analyzed the open charm production in the
exclusive binary reactions \bar{p}p\rightarrow \bar{Y}_cY_c, \bar{p}p\rightarrow D\bar{D} and \bar{p}p\rightarrow D\bar{D}^* at small momentum transfer.
Our consideration is based on a modified Regge type model,
motivated by quark-gluon string dynamics. The ... | {
"cite_spans": []
} | 10.1103/PhysRevC.78.025201 | 0807.1822 | Exclusive charm production in pbar p collisions at s^1/2 <15 GeV | [
"A. I. Titov",
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4a11b2d805a74a2da029ba214e3e7ac65001d36b | abstract | 0 | 16 | Abstract | Most real life systems have a random component: the multitude of endogenous
and exogenous factors influencing them result in stochastic fluctuations of the
parameters determining their dynamics. These empirical systems are in many
cases subject to noise of multiplicative nature. The special properties of
multiplicative... | {
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} | 0807.1823 | Cooperation Evolution in Random Multiplicative Environments | [
"Gur Yaari",
"Sorin Solomon"
] | [
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eaa6e2af2ed23c0fd4c91aedb28a08ba2596207c | subsection | 1 | 16 | Background and Previous Knowledge | One of the puzzling facts in game theory is the recurring result,
in a wide range of conditions that the general good is not reached
by each of the individuals following its own self interest.
Technically it means that in most of the games
considered, the “Nash Equilibrium” is not an optimal situation
for the ensemble ... | {
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... | 0807.1823 | Cooperation Evolution in Random Multiplicative Environments | [
"Gur Yaari",
"Sorin Solomon"
] | [
"q-fin.GN",
"physics.bio-ph",
"physics.soc-ph"
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9b538568d68acdd168e507d5cc698baa9e2ae9b6 | subsection | 2 | 16 | Background and Previous Knowledge | This is again a nontrivial consequence of the multiplicative dynamics: in usual additive gain/loss games one ends up in a globally non-optimize Nash equilibrium.
The attitude suggested by the analysis that follows is of ignoring events that never happen. It affects crucially the recommended level of sharing in very ris... | {
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"Gur Yaari",
"Sorin Solomon"
] | [
"q-fin.GN",
"physics.bio-ph",
"physics.soc-ph"
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990951408c82507f1cfdf234642c814eedaf7627 | subsection | 3 | 16 | The generic setup | First, in order to emphasize the particularities of the multiplicative random processes, let us evaluate the expected gain F(T) of a multiplicative random process up to time T. F(T) is by definition the sum over all possible histories H of duration T
of the probability of each history P(H) times the gain G(H) associate... | {
"cite_spans": []
} | 0807.1823 | Cooperation Evolution in Random Multiplicative Environments | [
"Gur Yaari",
"Sorin Solomon"
] | [
"q-fin.GN",
"physics.bio-ph",
"physics.soc-ph"
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992325fa26d0407ae93011ca1ee00cf9320796f1 | subsection | 4 | 16 | The generic setup | Since it is always true that M_a \ge M_g, it turns out that
the naïve (arithmetic) expectation is always deceiving by making
the game seemingly more gainful than it actually is. In the cases where
M_a \ge 1 \ge M_g it becomes a matter of life and death as the arithmetic mean predicts growth while
the reality follows th... | {
"cite_spans": []
} | 0807.1823 | Cooperation Evolution in Random Multiplicative Environments | [
"Gur Yaari",
"Sorin Solomon"
] | [
"q-fin.GN",
"physics.bio-ph",
"physics.soc-ph"
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0e7c1ee0118f51a9e5560a2ffe6d7013260ff8e8 | subsection | 5 | 16 | The generic setup | Combining these two observations with the knowledge of r_\infty leads to:r_N + D/(2N) \stackrel{_{\longrightarrow } }{_{N \rightarrow \infty }}r_\infty =\log {(p\cdot a+q\cdot b)}and allows one to evaluate the asymptotic dependence of r_N on N:r_N \sim \log {(p\cdot a+q\cdot b)} -D/(2N)This result is indeed validated b... | {
"cite_spans": []
} | 0807.1823 | Cooperation Evolution in Random Multiplicative Environments | [
"Gur Yaari",
"Sorin Solomon"
] | [
"q-fin.GN",
"physics.bio-ph",
"physics.soc-ph"
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c873c9a8f5f67cf19d999c4e75256ea05f306fba | subsection | 6 | 16 | Specific example | In the case where b \ne 0 and M_a>1 the decay can be avoided completely and forever. In order to build further the intuition for the generic case (b\ne 0) let us substitute the numbers p=q=0.5, a=2 and b=1/3 in the general process defined by equation REF . Here we have: M_a\equiv 7/6>1>M_g\equiv (2/3)^{(1/2)} For these... | {
"cite_spans": []
} | 0807.1823 | Cooperation Evolution in Random Multiplicative Environments | [
"Gur Yaari",
"Sorin Solomon"
] | [
"q-fin.GN",
"physics.bio-ph",
"physics.soc-ph"
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501a4febe7a19dd1e18a9d20f818327de086e58e | subsection | 7 | 16 | The Kelly terminology | As seen above, high risk, high gain potential processes generate a paradox: the naive expected wealth grows asymptotically to infinity while the probability
for non-vanishing wealth (the survival probability) decreases exponentially. To overcome this puzzle, J. Kelly, initiated an approach that led to a vast literature... | {
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... | 0807.1823 | Cooperation Evolution in Random Multiplicative Environments | [
"Gur Yaari",
"Sorin Solomon"
] | [
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"physics.bio-ph",
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a02fb86da554c2ea0cef9fc7367b72d34854bca1 | subsection | 8 | 16 | The Kelly terminology | For N of order 10 (and p=0.55,d=1), the region of ”dangerous“ f's shrinks from 0.8 (out of 1) to 10^{-20} !! (Figure REF ,inset C). This fact allows the player not only to win more asymptotically, but also to shrink significantly the risk one takes!
These results are presented in Figure REF .
[Figure: The curves in th... | {
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} | 0807.1823 | Cooperation Evolution in Random Multiplicative Environments | [
"Gur Yaari",
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] | [
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d329cbd7576a82e04782169f7cc1586abffbc000 | subsection | 9 | 16 | Effects of asynchronous updating:
infinite survival time for games with total loss | When the system has some kind of external clock one may treat it
in a synchronous fashion: i.e. all agents update their endowments
in the same instance. In many other systems the individuals are not
updated simultaneously but rather asynchronously.
The theoretical framework presented so far applies well to asynchronous... | {
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} | 0807.1823 | Cooperation Evolution in Random Multiplicative Environments | [
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5c896b0526742c294f29eb114100a9dad51ad339 | subsection | 10 | 16 | Effects of asynchronous updating:
infinite survival time for games with total loss | For N=20 sharing, synchronous individuals one gets close to the
ideal average r_{ideal}=\ln (\frac{3}{2}) (modulo disastrous collapses
after about 2^{20} \sim 10^6 steps which is not seen for
runs of order T=1000 as in figure REF ).
Asynchronous N=20 sharing individuals
exceed the naïve average rate (\ln (\frac{3}{2}))... | {
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} | 0807.1823 | Cooperation Evolution in Random Multiplicative Environments | [
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ba56bff13087563a5e3b9b9495db72c8881cb77c | subsection | 11 | 16 | Fixed group size and varied generosity. | Let us now fix the group size N and look at the asymptotic
growth rate. In particular, we look at the case in which after
each timestep one is donating to the other members of the group
a fraction 0 \ge D \ge 1 of the difference between one's wealth
and the average wealth of the group. In this way the accumulated wealt... | {
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7bd8af9a6bc943f857d081d0575441f46e2ed633 | subsection | 12 | 16 | Discussion | Altruism elicits in humans very powerful and diverse feelings. Its paradoxical nature makes it mysterious and challenging to understand. In fact, often one looks for hidden ulterior motives that would offer alternative explanations for an ostensibly altruistic behavior. Indeed, it is difficult to understand why a ratio... | {
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1a035dff998896ec6b51d69631f1988f498c1c13 | subsection | 13 | 16 | Conclusions | We have studied some aspects of the emergence, efficiency and consequences of cooperation in systems with multiplicative gains and losses.
We have found that as opposed to games with additive gains and losses, in a risky multiplicative environment unconditional cooperation is quite
a normal outcome. This conclusion is ... | {
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80b484b9929193593d7f6318eac9947da1ac574a | subsection | 14 | 16 | Appendix A: Average behavior vs. typical one | Let us show why the restoration of the arithmetic means requires exponential number of realizations:
to start with, we concentrate on the case where: a \ge 1 \ge b \ge 0 and M_a>1>M_g>0
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f11f7211cda7c9ee2487732ccfe692b4a589f76f | subsection | 15 | 16 | Appendix A: Average behavior vs. typical one | One can replace equation with a more general condition which requires contributions larger than the arithmetic mean:\frac{W(t)}{ W(0)} = a^n \cdot b^{t-n} > M_a^twhich yieldsR \sim e^{ t\lbrace \frac{\ln (M_a/b)}{\ln (a/b)}-p\rbrace ^2 /2pq}that generally means that the number of realizations needed to restore the (ari... | {
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428cdf91b85387e703f728053848f6f4ee7e8413 | abstract | 0 | 29 | Abstract | In this paper we deal with some properties of a class of semi-Riemannian
submersions between manifolds endowed with paraquaternionic structures, proving
a result of non-existence of paraquaternionic submersions between
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0d338afa338bc61ee62acdf9cc53f6073e8202ac | subsection | 1 | 29 | Introduction | The theory of (semi-)Riemannian submersions, as a “dual” of that of Riemannian immersions, is a relatively new and vast subject of study, which since its introduction made by O'Neill in , and indipendently by Gray in , has been continously developing, due to its growing importance in the physical framework which try to... | {
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e756b9c48d2b072d8884972ece7e579d66ce4b22 | subsection | 2 | 29 | Preliminaries | We recall some basic data about paraquaternionic manifolds. For a more detailed treatment of the subject, the reader is referred, for example, to , , and , and particularly, for the geometry of paracomplex structures, see and .Definition 2.1
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5d06e5e97d75516df098decc51b9810b267a1532 | subsection | 3 | 29 | Preliminaries | Then, if x\in M, choosing an h\in H such that x\in U_{h}, and putting \sigma _{x}=\mathrm {Span}_{\mathbb {R}}((J_{1}^{h})_{x},(J_{2}^{h})_{x},(J_{3}^{h})_{x}), we get a three dimensional vector subspace \sigma _x of End(T_{x}M), which does not depend on the open set U_{h} and on the structure (J_a^{h})_{a=1,2,3}, such... | {
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29546b26640a2d01e98424d89c1dcd1a39bc34ff | subsection | 4 | 29 | Preliminaries | Then, it is a paraquaternionic Kähler manifold if and only if for any x\in M there exists an open neighbourhood U of x on which a local basis (J_a)_{a=1,2,3} for \sigma is defined, such that the Levi-Civita connection verifies \nabla J_a=-\tau _c\omega _c\otimes J_b+\omega _b\otimes J_c, for any cyclic permutation (a,b... | {
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