Metod Saniga - Academia.edu (original) (raw)
Papers by Metod Saniga
Astrophysics and Space Science, 1993
AZh, Aug 1, 1992
It is assumed that a convective zone with sunspots can be considered as a unique analog of a type... more It is assumed that a convective zone with sunspots can be considered as a unique analog of a type-II superconductor with the presence of magnetic vortices. The mathematical formalism of Ginzburg and Landau is used to describe superconductivity, and a particular form of the Lagrangian is proposed for modeling macrophenomena. Although its physical content is different from that used in microphysics, the fundamental topological properties implied by both models are identical. It is demonstrated that the sunspot's umbra is analogous to the core of a superconductor vortex, and the penumbra has its counterpart in the vortex region, where the 'supercurrent' flows. It is also shown that the total magnetic flux of stable sunspots can have discrete values only.
Chaos Solitons & Fractals, Oct 1, 1998
It is demonstrated that the domain of the past of a pencil!generated temporal arrow over Galois _... more It is demonstrated that the domain of the past of a pencil!generated temporal arrow over Galois _elds of order q 1 "GF"q 1 ## incorporates the regions of both the past and the future of the arrow de_ned over its sub_eld GF"q#[ Þ 0887 Elsevier Science Ltd[ All rights reserved
Astronomische Nachrichten, 1996
We demonstrate that photons emitted by spiral galaxies become effectively massive, if the latter ... more We demonstrate that photons emitted by spiral galaxies become effectively massive, if the latter are treated as macroscopic Abelian Higgs topological solitons. The rest mass of a photon is shown to be proportional to the squared amplitude of the Higgs field distribution representing a 'backround' static cylindrically symmetric magnetic vorto-source (-sink). Because the amplitude increases in a monotonous fashion from zero a t the center of a spiral to a fixed non-zero value a t its outer boundary, the rest mass (group velocity) of photons emitted at shorter distances from the galaxy's center is smaller (greater) when compared to that of photons originating at larger distances. A rough estimate shows that for a spiral with a diameter of 60 kpc the maximum attainable mass of photon is of the order of K e y words: galaxiesmassive photons-Abelian Higgs solitons AAA subject classification: 157 g.
Linear Algebra and its Applications, Feb 1, 2020
Let T n (q) be the ring of lower triangular matrices of order n ≥ 2 with entries from the finite ... more Let T n (q) be the ring of lower triangular matrices of order n ≥ 2 with entries from the finite field F (q) of order q ≥ 2 and let 2 T n (q) denote its free left module. For n = 2, 3 it is shown that the projective line over T n (q) gives rise to a set of (q + 1) (n−1) q 3(n−1)(n−2) 2 affine planes of order q. The points of such an affine plane are non-free cyclic submodules of 2 T n (q) not contained in any non-unimodular free cyclic submodule of 2 T n (q) and its lines are points of the projective line. Furthermore, it is demonstrated that each affine plane can be extended to the projective plane of order q, with the 'line at infinity' being represented by those free cyclic submodules of 2 T n (q) that are generated by non-unimodular pairs. Our approach can straightforwardly be adjusted to address the case of arbitrary n.
Astrophysics and Space Science, Sep 1, 1993
We present a (2+1)-dimensional sunspot model whose Lagrange density contains, in addition to the ... more We present a (2+1)-dimensional sunspot model whose Lagrange density contains, in addition to the classical Maxwellian term, the so-called Chern-Simons term generalized here in a gauge-invariant way. It is shown that it is namely this term which is responsible for the confinement of the spot's electromagnetic field into a finite-dimensional domain. We further demonstrate that besides the total magnetic flux it is also the spot's electric charge which is non-zero and that both quantities are topologically quantized, i.e. can acquire discrete values only. Finally, a cylindrically symmetric sunspot carryingp magnetic flux quanta,p being a positive integer, is revealed to possess a non-zero total angular momentum, the magnitude of which is proportional top2. The latter fact also implies the stability of rotating sunspots against their fragmentation (splitting).
Chaos Solitons & Fractals, May 1, 2002
It is pointed out that the hierarchy of fractal dimensions characterizing transfinite heterotic s... more It is pointed out that the hierarchy of fractal dimensions characterizing transfinite heterotic string spacetimes bears a striking resemblance to the sequence of the number of lines lying on Del Pezzo surfaces. Employing the notion and properties of the so-called Cantorian fractal space, E (∞) , El Naschie has recently demonstrated [1-6] that the transfinite heterotic string spacetimes are endowed with the following five characteristic fractal dimensions
Journal of Geometry, Dec 28, 2008
Given a ring of ternions R, i. e., a ring isomorphic to that of upper triangular 2 × 2 matrices w... more Given a ring of ternions R, i. e., a ring isomorphic to that of upper triangular 2 × 2 matrices with entries from an arbitrary commutative field F , a complete classification is performed of the vectors from the free left R-module R n+1 , n ≥ 1, and of the cyclic submodules generated by these vectors. The vectors fall into 5 + |F | and the submodules into 6 distinct orbits under the action of the general linear group GLn+1(R). Particular attention is paid to free cyclic submodules generated by non-unimodular vectors, as these are linked with the lines of PG(n, F), the n-dimensional projective space over F. In the finite case, F = GF(q), explicit formulas are derived for both the total number of non-unimodular free cyclic submodules and the number of such submodules passing through a given vector. These formulas yield a combinatorial approach to the lines and points of PG(n, q), n ≥ 2, in terms of vectors and non-unimodular free cyclic submodules of R n+1 .
Astrophysics and Space Science, Feb 1, 1993
ABSTRACT
Springer eBooks, Nov 19, 2005
ABSTRACT
Contributions of The Astronomical Observatory Skalnate Pleso, Jul 1, 1992
ABSTRACT
Chaos Solitons & Fractals, Jul 1, 1998
This paper highlights the most remarkable properties of pencil!generated temporal dimensions over... more This paper highlights the most remarkable properties of pencil!generated temporal dimensions over Galois _elds of even characteristic "GF"1 n ##[ It is shown that in the _eld of real numbers the ordinary arrow of time emerges in GF"1 n # either as a peculiar temporal arrow featuring the domains of the past and future\ but lacking the moment of the present\ or as an observable spatial dimension[ In order to understand these peculiarities more fully a quite detailed account is presented of the properties of a point!conic in projective planes over Galois _elds of both even and odd order[
Designs, Codes and Cryptography, Jun 3, 2011
Invariant notions of a class of Segre varieties S (m) (2) of PG(2 m − 1, 2) that are direct produ... more Invariant notions of a class of Segre varieties S (m) (2) of PG(2 m − 1, 2) that are direct products of m copies of PG(1, 2), m being any positive integer, are established and studied. We first demonstrate that there exists a hyperbolic quadric that contains S (m) (2) and is invariant under its projective stabiliser group G S (m) (2). By embedding PG(2 m − 1, 2) into PG(2 m − 1, 4), a basis of the latter space is constructed that is invariant under G S (m) (2) as well. Such a basis can be split into two subsets of an odd and even parity whose spans are either real or complex-conjugate subspaces according as m is even or odd. In the latter case, these spans can, in addition, be viewed as indicator sets of a G S (m) (2)-invariant geometric spread of lines of PG(2 m − 1, 2). This spread is also related with a G S (m) (2)-invariant non-singular Hermitian variety. The case m = 3 is examined in detail to illustrate the theory. Here, the lines of the invariant spread are found to fall into four distinct orbits under G S (3) (2) , while the points of PG(7, 2) form five orbits.
HAL (Le Centre pour la Communication Scientifique Directe), 2012
We reveal an intriguing connection between the set of 27 (disregarding the identity) invertible s... more We reveal an intriguing connection between the set of 27 (disregarding the identity) invertible symmetric 3 × 3 matrices over GF(2) and the points of the generalized quadrangle GQ(2, 4). The 15 matrices with eigenvalue one correspond to a copy of the subquadrangle GQ(2, 2), whereas the 12 matrices without eigenvalues have their geometric counterpart in the associated double-six. The fine details of this correspondence, including the precise algebraic meaning/analogue of collinearity, are furnished by employing the representation of GQ(2, 4) as a quadric in PG(5, 2) of projective index one. An interesting physical application of our findings is also mentioned.
International Journal of Geometric Methods in Modern Physics, Feb 1, 2011
The Veldkamp space, in the sense of Buekenhout and Cohen, of the generalized quadrangle GQ(4, 2) ... more The Veldkamp space, in the sense of Buekenhout and Cohen, of the generalized quadrangle GQ(4, 2) is shown not to be a (partial) linear space by simply giving several examples of Veldkamp lines (V-lines) having two or even three Veldkamp points (V-points) in common. Alongside the ordinary V-lines of size five, one also finds V-lines of cardinality three and two. There, however, exists a subspace of the Veldkamp space isomorphic to PG(3, 4) having 45 perps and 40 plane ovoids as its 85 V-points, with its 357 V-lines being of four distinct types. A V-line of the first type consists of five perps on a common line (altogether 27 of them), the second type features three perps and two ovoids sharing a tricentric triad (240 members), whilst the third and fourth type each comprises a perp and four ovoids in the rosette centered at the (common) center of the perp (90). It is also pointed out that 160 non-plane ovoids (tripods) fall into two distinct orbits-of sizes 40 and 120with respect to the stabilizer group of a copy of GQ(2, 2); a tripod of the first/second orbit sharing with the GQ(2, 2) a tricentric/unicentric triad, respectively. Finally, three remarkable subconfigurations of V-lines represented by fans of ovoids through a fixed ovoid are examined in some detail.
The paper presents, to our knowledge, a first fairly comprehensive and mathematically well-underp... more The paper presents, to our knowledge, a first fairly comprehensive and mathematically well-underpinned classification of the psychopathology of time (and space). After reviewing the most illustrative first-person accounts of "anomalous/peculiar" experiences of time (and, to a lesser degree, space) we introduce and describe in detail their algebraic geometrical model. The model features six qualitatively different types of the internal structure of time dimension and four types of that of space. As for time, the most pronounced are the ordinary "past-present-future," "present-only" ("eternal/everlasting now") and "no-present" (time "standing still") patterns. Concerning space, the most elementary are the ordinary, i.e., "here-and-there," mode and the "here-only" one ("omnipresence"). We then show what the admissible combinations of temporal and spatial psycho-patterns are and give a rigorous algebraic geometrical classification of them. The predictive power of the model is illustrated by the phenomenon of psychological timereversal and the experiential difference between time and space. The paper ends with a brief account of some epistemological/ontological questions stemming from the approach.
Astrophysics and Space Science, 1992
We demonstrate that a spot-connected prominence (filament) can simply be viewed as manifestation ... more We demonstrate that a spot-connected prominence (filament) can simply be viewed as manifestation of a non-trivial topology of the spot's Higgs vacuum. It is conjectured that the spot-connected prominence forms in the region where the phase of the Higgs field, describing sunspot, has its discontinuity. A conclusion is arrived at that two topologically different types of prominences associated with sunspots might exist; a one-arm prominence, entering the spot from one side only, and a two-arm one, which points towards the spot's center from two opposite directions and whose each arm carries a topological charge whose magnitude is one-half of that carried by the former.
Astrophysics and Space Science, 1993
AZh, Aug 1, 1992
It is assumed that a convective zone with sunspots can be considered as a unique analog of a type... more It is assumed that a convective zone with sunspots can be considered as a unique analog of a type-II superconductor with the presence of magnetic vortices. The mathematical formalism of Ginzburg and Landau is used to describe superconductivity, and a particular form of the Lagrangian is proposed for modeling macrophenomena. Although its physical content is different from that used in microphysics, the fundamental topological properties implied by both models are identical. It is demonstrated that the sunspot's umbra is analogous to the core of a superconductor vortex, and the penumbra has its counterpart in the vortex region, where the 'supercurrent' flows. It is also shown that the total magnetic flux of stable sunspots can have discrete values only.
Chaos Solitons & Fractals, Oct 1, 1998
It is demonstrated that the domain of the past of a pencil!generated temporal arrow over Galois _... more It is demonstrated that the domain of the past of a pencil!generated temporal arrow over Galois _elds of order q 1 "GF"q 1 ## incorporates the regions of both the past and the future of the arrow de_ned over its sub_eld GF"q#[ Þ 0887 Elsevier Science Ltd[ All rights reserved
Astronomische Nachrichten, 1996
We demonstrate that photons emitted by spiral galaxies become effectively massive, if the latter ... more We demonstrate that photons emitted by spiral galaxies become effectively massive, if the latter are treated as macroscopic Abelian Higgs topological solitons. The rest mass of a photon is shown to be proportional to the squared amplitude of the Higgs field distribution representing a 'backround' static cylindrically symmetric magnetic vorto-source (-sink). Because the amplitude increases in a monotonous fashion from zero a t the center of a spiral to a fixed non-zero value a t its outer boundary, the rest mass (group velocity) of photons emitted at shorter distances from the galaxy's center is smaller (greater) when compared to that of photons originating at larger distances. A rough estimate shows that for a spiral with a diameter of 60 kpc the maximum attainable mass of photon is of the order of K e y words: galaxiesmassive photons-Abelian Higgs solitons AAA subject classification: 157 g.
Linear Algebra and its Applications, Feb 1, 2020
Let T n (q) be the ring of lower triangular matrices of order n ≥ 2 with entries from the finite ... more Let T n (q) be the ring of lower triangular matrices of order n ≥ 2 with entries from the finite field F (q) of order q ≥ 2 and let 2 T n (q) denote its free left module. For n = 2, 3 it is shown that the projective line over T n (q) gives rise to a set of (q + 1) (n−1) q 3(n−1)(n−2) 2 affine planes of order q. The points of such an affine plane are non-free cyclic submodules of 2 T n (q) not contained in any non-unimodular free cyclic submodule of 2 T n (q) and its lines are points of the projective line. Furthermore, it is demonstrated that each affine plane can be extended to the projective plane of order q, with the 'line at infinity' being represented by those free cyclic submodules of 2 T n (q) that are generated by non-unimodular pairs. Our approach can straightforwardly be adjusted to address the case of arbitrary n.
Astrophysics and Space Science, Sep 1, 1993
We present a (2+1)-dimensional sunspot model whose Lagrange density contains, in addition to the ... more We present a (2+1)-dimensional sunspot model whose Lagrange density contains, in addition to the classical Maxwellian term, the so-called Chern-Simons term generalized here in a gauge-invariant way. It is shown that it is namely this term which is responsible for the confinement of the spot's electromagnetic field into a finite-dimensional domain. We further demonstrate that besides the total magnetic flux it is also the spot's electric charge which is non-zero and that both quantities are topologically quantized, i.e. can acquire discrete values only. Finally, a cylindrically symmetric sunspot carryingp magnetic flux quanta,p being a positive integer, is revealed to possess a non-zero total angular momentum, the magnitude of which is proportional top2. The latter fact also implies the stability of rotating sunspots against their fragmentation (splitting).
Chaos Solitons & Fractals, May 1, 2002
It is pointed out that the hierarchy of fractal dimensions characterizing transfinite heterotic s... more It is pointed out that the hierarchy of fractal dimensions characterizing transfinite heterotic string spacetimes bears a striking resemblance to the sequence of the number of lines lying on Del Pezzo surfaces. Employing the notion and properties of the so-called Cantorian fractal space, E (∞) , El Naschie has recently demonstrated [1-6] that the transfinite heterotic string spacetimes are endowed with the following five characteristic fractal dimensions
Journal of Geometry, Dec 28, 2008
Given a ring of ternions R, i. e., a ring isomorphic to that of upper triangular 2 × 2 matrices w... more Given a ring of ternions R, i. e., a ring isomorphic to that of upper triangular 2 × 2 matrices with entries from an arbitrary commutative field F , a complete classification is performed of the vectors from the free left R-module R n+1 , n ≥ 1, and of the cyclic submodules generated by these vectors. The vectors fall into 5 + |F | and the submodules into 6 distinct orbits under the action of the general linear group GLn+1(R). Particular attention is paid to free cyclic submodules generated by non-unimodular vectors, as these are linked with the lines of PG(n, F), the n-dimensional projective space over F. In the finite case, F = GF(q), explicit formulas are derived for both the total number of non-unimodular free cyclic submodules and the number of such submodules passing through a given vector. These formulas yield a combinatorial approach to the lines and points of PG(n, q), n ≥ 2, in terms of vectors and non-unimodular free cyclic submodules of R n+1 .
Astrophysics and Space Science, Feb 1, 1993
ABSTRACT
Springer eBooks, Nov 19, 2005
ABSTRACT
Contributions of The Astronomical Observatory Skalnate Pleso, Jul 1, 1992
ABSTRACT
Chaos Solitons & Fractals, Jul 1, 1998
This paper highlights the most remarkable properties of pencil!generated temporal dimensions over... more This paper highlights the most remarkable properties of pencil!generated temporal dimensions over Galois _elds of even characteristic "GF"1 n ##[ It is shown that in the _eld of real numbers the ordinary arrow of time emerges in GF"1 n # either as a peculiar temporal arrow featuring the domains of the past and future\ but lacking the moment of the present\ or as an observable spatial dimension[ In order to understand these peculiarities more fully a quite detailed account is presented of the properties of a point!conic in projective planes over Galois _elds of both even and odd order[
Designs, Codes and Cryptography, Jun 3, 2011
Invariant notions of a class of Segre varieties S (m) (2) of PG(2 m − 1, 2) that are direct produ... more Invariant notions of a class of Segre varieties S (m) (2) of PG(2 m − 1, 2) that are direct products of m copies of PG(1, 2), m being any positive integer, are established and studied. We first demonstrate that there exists a hyperbolic quadric that contains S (m) (2) and is invariant under its projective stabiliser group G S (m) (2). By embedding PG(2 m − 1, 2) into PG(2 m − 1, 4), a basis of the latter space is constructed that is invariant under G S (m) (2) as well. Such a basis can be split into two subsets of an odd and even parity whose spans are either real or complex-conjugate subspaces according as m is even or odd. In the latter case, these spans can, in addition, be viewed as indicator sets of a G S (m) (2)-invariant geometric spread of lines of PG(2 m − 1, 2). This spread is also related with a G S (m) (2)-invariant non-singular Hermitian variety. The case m = 3 is examined in detail to illustrate the theory. Here, the lines of the invariant spread are found to fall into four distinct orbits under G S (3) (2) , while the points of PG(7, 2) form five orbits.
HAL (Le Centre pour la Communication Scientifique Directe), 2012
We reveal an intriguing connection between the set of 27 (disregarding the identity) invertible s... more We reveal an intriguing connection between the set of 27 (disregarding the identity) invertible symmetric 3 × 3 matrices over GF(2) and the points of the generalized quadrangle GQ(2, 4). The 15 matrices with eigenvalue one correspond to a copy of the subquadrangle GQ(2, 2), whereas the 12 matrices without eigenvalues have their geometric counterpart in the associated double-six. The fine details of this correspondence, including the precise algebraic meaning/analogue of collinearity, are furnished by employing the representation of GQ(2, 4) as a quadric in PG(5, 2) of projective index one. An interesting physical application of our findings is also mentioned.
International Journal of Geometric Methods in Modern Physics, Feb 1, 2011
The Veldkamp space, in the sense of Buekenhout and Cohen, of the generalized quadrangle GQ(4, 2) ... more The Veldkamp space, in the sense of Buekenhout and Cohen, of the generalized quadrangle GQ(4, 2) is shown not to be a (partial) linear space by simply giving several examples of Veldkamp lines (V-lines) having two or even three Veldkamp points (V-points) in common. Alongside the ordinary V-lines of size five, one also finds V-lines of cardinality three and two. There, however, exists a subspace of the Veldkamp space isomorphic to PG(3, 4) having 45 perps and 40 plane ovoids as its 85 V-points, with its 357 V-lines being of four distinct types. A V-line of the first type consists of five perps on a common line (altogether 27 of them), the second type features three perps and two ovoids sharing a tricentric triad (240 members), whilst the third and fourth type each comprises a perp and four ovoids in the rosette centered at the (common) center of the perp (90). It is also pointed out that 160 non-plane ovoids (tripods) fall into two distinct orbits-of sizes 40 and 120with respect to the stabilizer group of a copy of GQ(2, 2); a tripod of the first/second orbit sharing with the GQ(2, 2) a tricentric/unicentric triad, respectively. Finally, three remarkable subconfigurations of V-lines represented by fans of ovoids through a fixed ovoid are examined in some detail.
The paper presents, to our knowledge, a first fairly comprehensive and mathematically well-underp... more The paper presents, to our knowledge, a first fairly comprehensive and mathematically well-underpinned classification of the psychopathology of time (and space). After reviewing the most illustrative first-person accounts of "anomalous/peculiar" experiences of time (and, to a lesser degree, space) we introduce and describe in detail their algebraic geometrical model. The model features six qualitatively different types of the internal structure of time dimension and four types of that of space. As for time, the most pronounced are the ordinary "past-present-future," "present-only" ("eternal/everlasting now") and "no-present" (time "standing still") patterns. Concerning space, the most elementary are the ordinary, i.e., "here-and-there," mode and the "here-only" one ("omnipresence"). We then show what the admissible combinations of temporal and spatial psycho-patterns are and give a rigorous algebraic geometrical classification of them. The predictive power of the model is illustrated by the phenomenon of psychological timereversal and the experiential difference between time and space. The paper ends with a brief account of some epistemological/ontological questions stemming from the approach.
Astrophysics and Space Science, 1992
We demonstrate that a spot-connected prominence (filament) can simply be viewed as manifestation ... more We demonstrate that a spot-connected prominence (filament) can simply be viewed as manifestation of a non-trivial topology of the spot's Higgs vacuum. It is conjectured that the spot-connected prominence forms in the region where the phase of the Higgs field, describing sunspot, has its discontinuity. A conclusion is arrived at that two topologically different types of prominences associated with sunspots might exist; a one-arm prominence, entering the spot from one side only, and a two-arm one, which points towards the spot's center from two opposite directions and whose each arm carries a topological charge whose magnitude is one-half of that carried by the former.
For N ≥ 2, an N-qubit doily is a doily living in the N-qubit symplectic polar space. These doilie... more For N ≥ 2, an N-qubit doily is a doily living in the N-qubit symplectic polar space. These doilies are related to operator-based proofs of quantum contextuality. Following and extending the strategy of Saniga et al. (Mathematics 9 (2021) 2272) that focused exclusively on three-qubit doilies, we first bring forth several formulas giving the number of both linear and quadratic doilies for any N > 2. Then we present an effective algorithm for the generation of all N-qubit doilies. Using this algorithm for N = 4 and N = 5, we provide a classification of N-qubit doilies in terms of types of observables they feature and number of negative lines they are endowed with. We also list several distinguished findings about N-qubit doilies that are absent in the three-qubit case, point out a couple of specific features exhibited by linear doilies and outline some prospective extensions of our approach.