Narrow Results

The paper investigates inequalities between the numbers of different (scattered) subword occurrences. The Parikh matrix recently introduced is an efficient tool. We give various characterizations for Parikh matrices. Of special interest is the case where the matrix determines the word uniquely. We investigate such matrix unambiguous words. The considerations are extended to concern languages. Several open problems and problem areas are indicated.

For certain problems (for example, computing repetitions and repeats, data compression applications) it is not necessary that the suffixes of a string represented in a suffix tree or suffix array should occur in lexicographical order (lexorder). It thus becomes of interest to study possible alternate orderings of the suffixes in these data structures, that may be easier to construct or more efficient to use. In this paper we consider the "reconstruction" of a suffix array based on a given reordering of the alphabet, and we describe simple time- and space-efficient algorithms that accomplish it.

We say a family of strings over an alphabet is an UMFF if every string has a unique maximal factorization over . Foundational work by Chen, Fox and Lyndon established properties of the Lyndon circ-UMFF, which is based on lexicographic ordering. Commencing with the circ-UMFF related to V-order, we then proved analogous factorization families for a further 32 Block-like binary orders. Here we distinguish between UMFFs and circ-UMFFs, and then study the structural properties of circ-UMFFs. These properties give rise to the complete construction of any circ-UMFF. We prove that any circ-UMFF is a totally ordered set and a factorization over it must be monotonic. We define atom words and initiate a study of u, v-atoms. Applications of circ-UMFFs arise in string algorithmics.

Crochemore's repetitions algorithm introduced in 1981 was the first O(n log n) algorithm for computing repetitions. Since then, several linear-time worst-case algorithms for computing runs have been introduced. They all follow a similar strategy: first compute the suffix tree or array, then use the suffix tree or array to compute the Lempel-Ziv factorization, then using the Lempel-Ziv factorization compute all the runs. It is conceivable that in practice an extension of Crochemore's repetitions algorithm may outperform the linear-time algorithms, or at least for certain classes of strings. The nature of Crochemore's algorithm lends itself naturally to parallelization, while the linear-time algorithms are not easily conducive to parallelization. For all these reasons it is interesting to explore ways to extend the original Crochemore's repetitions algorithm to compute runs. We present three variants of extending the repetitions algorithm to compute runs: two with a worsen complexity of O(n (log n)²), and one with the same complexity as the original algorithm. The three variants are tested for speed of performance and their memory requirements are analyzed. The third variant is tested and analyzed for various memory-saving alterations. The purpose of this research is to identify the best extension of Crochemore's algorithm for further study, comparison with other algorithms, and parallel implementation.

A nonempty circular string C(x) of length n is said to be covered by a set U_k of strings each of fixed length k≤n iff every position in C(x) lies within an occurrence of some string u∈U_k. In this paper we consider the problem of determining the minimum cardinality of a set U_k which guarantees that every circular string C(x) of length n≥k can be covered. In particular, we show how, for any positive integer m, to choose the elements of U_k so that, for sufficiently large k, u_k≈σ^k–m, where u_k=|U_k| and σ is the size of the alphabet on which the strings are defined. The problem has application to DNA sequencing by hybridization using oligonucleotide probes.

We discuss the shape of the interaction region of the elastically scattered protons stipulated by the high-energy Pomeron exchange which turns out to be very similar with the shape of the static string representing the confining QCD flux tube. This similarity disappears when we enter the LHC energy region, which corresponds to many-Pomeron exchanges. Reversing the argument we conjecture a modified relationship between the width and the length of the confining string at very large lengths.

Modeling the worldsheets along the trajectory (a string) of a point particle (a 0-brane) as two timelike surfaces in 3-subspace of Minkowskian spacetime, respectively, the work aims at analyzing the topological structures of these two worldsheets along the trajectory of the point particle from the view point of singularity theory. Different from the regular curves, the traveling trajectory (modeled as framed timelike curve) of the particle is allowed to be singular, two worldsheets are generated by the traveling trajectories of the particle. As applications of singularity theory, we classify the singularities of these two worldsheets along the traveling trajectory of the particle. Using the approach of the unfolding theory in singularity theory, we find two new geometric invariants which are useful for characterizing the local topological structures of singularities of these two worldsheets along the particle. It is revealed that there exist cuspidal edge type and swallowtail type of singularities for these two worldsheets under the appropriate conditions of geometric invariants. Meanwhile, it is also pointed out that the types of singularities of these two worldsheets have a close relationships to the order of contacts between these two worldsheets and two timelike planes, respectively. Finally, some examples are presented to interpret our theoretical results.

In this paper we suggest a new model of preons–dyons making composite quark–leptons and bosons, described by the supersymmetric string-inspired flipped gauge group of symmetry. This approach predicts the possible extension of the Standard Model to the family replicated gauge group model of type G^N_fam, where N_fam is the number of families and G is the symmetry group: G = SMG, SU(5), SO(10), E₆, etc. Here E₆ and are nondual and dual sectors of theory with hyperelectric g and hypermagnetic charges, respectively. Starting with an idea that the most realistic model leading to the unification of all fundamental interactions (including gravity) is the "heterotic" string-derived flipped model, we have assumed that at high energies μ > 10¹⁶GeV there exists the following chain of the flipped models:

It is known that gravitational and electromagnetic fields of an electron are described by the ultra-extreme Kerr-Newman (KN) black hole solution with extremely high spin/mass ratio. This solution is singular and has a topological defect, the Kerr singular ring, which may be regularized by introducing the solitonic source based on the Higgs mechanism of symmetry breaking. The source represents a domain wall bubble interpolating between the flat region inside the bubble and external KN solution. It was shown recently that the source represents a supersymmetric bag model, and its structure is unambiguously determined by Bogomolnyi equations. The Dirac equation is embedded inside the bag consistently with twistor structure of the Kerr geometry, and acquires the mass from the Yukawa coupling with Higgs field. The KN bag turns out to be flexible, and for parameters of an electron, it takes the form of very thin disk with a circular string placed along sharp boundary of the disk. Excitation of this string by a traveling wave creates a circulating singular pole, indicating that the bag-like source of KN solution unifies the dressed and point-like electron in a single bag-string-quark system.

After Dirac introduced the monopole, topological objects have played increasingly important roles in physics. In this review we discuss the role of the knot, the most sophisticated topological object in physics, and related topological objects in various areas in physics. In particular, we discuss how the knots appear in Maxwell’s theory, Skyrme theory, and multicomponent condensed matter physics.

In processing a page image by a given zoning algorithm (automatic or manual), a certain text string is generated which may not be the same as the correct string. The difference may be due to the incorrect reading order selected by the employed zoning algorithm or poor recognition of characters. A difference algorithm is commonly used to find the best match between the generated string and the correct string. The output of such an algorithm will then be a sequence of matched substrings which are not in the correct order. To determine the performance of a given zoning algorithm, it is of interest to find the minimum number of moves needed to obtain the correct string from the string generated by that algorithm. The problem can be modeled as a sorting problem where a string of n integers ordered in a random manner, must be sorted in ascending (or descending) order. In this paper, we derive bounds on the time complexity of sorting a given string and present a near-optimal algorithm for that.

In this paper, we have examined charged strange quark matter attached to the string cloud in the spherical symmetric space–time admitting one-parameter group of conformal motions. For this purpose, we have solved Einstein's field equations for spherical symmetric space–time with strange quark matter attached to the string cloud via conformal motions. Also, we have discussed the features of the obtained solutions.

We argue that $p_T$ distribution data from the LHC on the invariant differential yield of the charged primary particles in $pp$ collisions at $\sqrt{s}=0.9\mathrm{\text{TeV}},2.76\mathrm{\text{TeV}},7\mathrm{\text{TeV}}$ and in Pb–Pb collisions at $\sqrt{s_{NN}}=2.76$TeV with six centrality bins contains several $p_T$ regions with special properties. These distributions were analyzed by fitting the data with exponential functions. We conclude that the regions reflect features of fragmentation and hadronization of partons through the string dynamics. The nuclear transparency results in negligible influence of the medium in the III region ($p_T>17-20\mathrm{\text{GeV/c}}$), which has highest $p_T$ values. The effects and changes by the medium start to appear weakly in the II region ($4-6\mathrm{\text{GeV/c}}<p_T<17-20\mathrm{\text{GeV/c}}$) and become stronger in the I region ($p_T<4-6\mathrm{\text{GeV/c}}$). It seems that the II region has highest number of strings. The increase in string density in this region could lead to fusion of strings, appearance of a new string and collective behavior of the partons in the most central collisions. These phenomena can explain anomalous behavior of the Nuclear Modification Factor in the II region. We propose the II region as a possible area of Quark Gluon Plasma formation through string fusion. The first $p_T$ regions are the ones with the maximum number of hadrons and minimum number of strings due to direct hadronization of the low energy strings into two quark systems–mesons.

The inclusive spectrum of the charged particles, $\pi$⁰- and $\eta$-mesons produced in the pp collisions at LHC energies were analyzed by fitting them with exponential functions. It was found the spectra were composed of several p${}_T$ regions, which could be characterized by the length of the regions $L_K^c$ and two free fitting parameters $a_K^c$ and $b_K^c$. The study of the $L_K^c$ dependences of the parameters $a_K^c$ and $b_K^c$ and of the energy dependencies of the $L_K^c$, $a_K^c$ and $b_K^c$ showed that the regions can be classified into two groups depending on the values of the $L_K^c$, $a_K^c$ and $b_K^c$. The values of the $L_K^c$ and $b_K^c$ for the first group don’t depend on colliding energy and the type of the particles (though the values of $a_K^c$ increase linearly with energy) whereas the characteristics in the second group of regions show strong dependencies. It was found that the ratio of the length for the $\eta$-mesons to one for the $\pi$⁰-mesons is approximately equal to the ratio of their mass: $〈L_{\eta }〉:〈L_{{\pi }^0}〉\cong m_{\eta }:m_{{\pi }^0}$. Assuming that the values of the $L_K^c$ are directly proportional to the string tension the result could be considered as evidence in favor of parton string fragmentation dynamics. The increase in the lengths for the $\eta$-mesons’ regions is accompanied by an increase of the values for the parameter $b_k^c$. It can mean that the $\eta$-mesons were produced at smaller values of ${\alpha }_S$ compared with that for $\pi$⁰-mesons. The results show that for the first group of regions the lengths of the regions are $\sim$3–5 times greater than the lengths of neighboring, lower p${}_T$ regions. For the second group of regions the lengths of the regions are $\sim$1–2 times greater than the lengths of neighboring lower p${}_T$ region. In the framework of the string fragmentation and hadronization dynamics, this could mean that the particles in the group $I$ of regions are produced through previous-generation strings decays into $\sim$3–5 strings while those in group $II$ originate from previous-generation strings decays into $\sim$2 strings.

Principal component analysis (PCA) has been successfully applied in structural dynamics in recent years. However, it is usually used as a black-box, resulting in a gap between the application aspect and the physics essence of the problem. Thus a physical interpretation of PCA is necessary, along with further investigation, especially on the mechanism involved. This paper provides a physical meaning of the PCA by the theoretical analysis and numerical experiment on the vibration of a 1D string. Conditions that make the interpretation feasible were identified. The theoretical derivation and numerical simulation results indicate that the PCA gives a good estimation of the modal participation ratio in terms of energy, and the principal component coefficient (PCC) can be used to estimate the structural modes. The physical interpretation gives a new perspective on how the current methods work while providing the possibility of further application of the PCA related methods to structural dynamic problems.

Recently the strings and the string number of self-maps were used in the computation of the algebraic entropy of specific abelian group endomorphisms. We introduce two special kinds of strings, and their relative string numbers. We show that a dichotomy holds for all these three string numbers; in fact, they admit only zero and infinity as values on abelian group endomorphisms.

The characteristics of the replication is investigated in this paper. By invoking the Potts model versus holographic superconductors for “gauge” versus “string”, the pair forms as a duality in natural manner. It can be shown that resulted characteristics of replication hence deserves to be called as an Autopoietic Smart Grid. Furthermore, we are able to trace the factors contributed to these characteristics; the autopoiesis is contributed via gauge self-energy; the surveillance is due to Maxwell’s demon; the organizational adaptivity is due to the communication capacity of the string and the oscillations of the gauge. Finally, it can also be shown that such a Smart Grid replication exists as long as the string is stable and gauge is synchronized.

Let $A(G)$ be the adjacency matrix of a graph $G$. Let $s(v)$ denote the row entries of $A(G)$ corresponding to the vertex $v$ of $G$. The Hamming distance between the strings $s(u)$ and $s(v)$ is the number of positions in which $s(u)$ and $s(v)$ differ. In this paper, we study the Hamming distance between the strings generated by the adjacency matrix of subgraph complement of a graph. We also compute sum of Hamming distances between all pairs of strings generated by the adjacency matrix of $G\oplus S$.

In this paper the mass of a universe, which began as a gravitationally closed, maximally spinning, Planck density quantum string is derived.

A universe beginning in such an initial state has been called a Super Spin Model universe. The total mass, M, of the Super Spin Model universe is shown to be a function of only four fundamental parameters ħ, c, G, e, such that: M = 4π²(ħc/G)^1/2 exp(ħc/e²).

The present paper primarily consists of a brief derivation of the above equation and a short synopsis of the Super Spin Model.

During formation fracturing in super deep wells, the working string must withstand tremendous differences in temperature and pressure. For safety purposes, slip joints and hydraulic anchors are often used. In this paper, the mechanical behavior of the tubular string was modeled according to the working process. Based on data from a high pressure, high temperature super deep exploratory well in Tahe Oilfield in west China, tubing string axial deformation and axial force at key points were calculated in both a normal fracturing and a sand plugging state. Subsequent analysis showed that: change in temperature is the most important inducement to string axial contraction; multiple slip joints should be used and be set in compression state before fluid injection; hydraulic anchors are less reliable and should be paid more attention; and parameters in sand plugging state should be highlighted in down hole tools selection.