Let <i>f</i>(u) and <i>g</i>(v) be two polynomials of degree <i>k</i> and <i>l</i> respectively, not both linear which split into distinct linear factors over F<sub&g...Let <i>f</i>(u) and <i>g</i>(v) be two polynomials of degree <i>k</i> and <i>l</i> respectively, not both linear which split into distinct linear factors over F<sub>q</sub>. Let <img src="Edit_83041428-d8b0-4505-8c3c-5e29f2886159.png" width="160" height="15" alt="" /> be a finite commutative non-chain ring. In this paper, we study polyadic codes and their extensions over the ring <i>R</i>. We give examples of some polyadic codes which are optimal with respect to Griesmer type bound for rings. A Gray map is defined from <img src="Edit_c75f119d-3176-4a71-a36a-354955044c09.png" width="50" height="15" alt="" /> which preserves duality. The Gray images of polyadic codes and their extensions over the ring <i>R</i> lead to construction of self-dual, isodual, self-orthogonal and complementary dual (LCD) codes over F<i><sub>q</sub></i>. Some examples are also given to illustrate this.展开更多
The architectural development of Acacia karroo conforms to Troll’s model. Growth of the branches is modular and sympodial with heteroblastic leaves on all long shoots of the tree, including the seedling. Axillary bud...The architectural development of Acacia karroo conforms to Troll’s model. Growth of the branches is modular and sympodial with heteroblastic leaves on all long shoots of the tree, including the seedling. Axillary buds tend to proliferate especially on flowering shoots where they form fascicles consisting of up to 10 inflorescences arranged in two parallel serial rows per leaf axil. Most axillary buds are sylleptic and basal buds which give rise to short shoots, each producing two to five cataphylls each season, but no flowers. Inflorescences are only produced on long shoots (modules) of the current season. After flowering the terminal part of the module aborts, trees are usually andromonoecious with capitate inflorescences containing 40 to 100 flowers each, with some male and some hermaphrodite. Some trees produce only male flowers. Anthesis in the same inflorescence, the same tree as well as amongst trees of the same community are synchronised and occur at intermittent intervals, each lasting three or more days at a time. Flowers are protogynous and pollen is produced in polyads, each consisting of 16 pollen grains. Ovaries contain 10 to 14 ovules each. The concave stigma has space for only one polyad which can fertilise all ovules in the ovary after a single pollination event. Fruit set is low with 0 to 10 fruits (pods) per inflorescence.展开更多
Modern magnetic resonance imaging(MRI)experiments require simultaneous spin and spatial dynamics treatment.This paper aims to demonstrate the possibility of simulating a large spin system for diffusion-weighted MRI ex...Modern magnetic resonance imaging(MRI)experiments require simultaneous spin and spatial dynamics treatment.This paper aims to demonstrate the possibility of simulating a large spin system for diffusion-weighted MRI experiments.The numerical simulation of diffusion MRI depends on Bloch-Torrey equations.The latter describe the behavior of spin systems under the influence of magnetic fields and diffusion processes.They are particularly relevant in magnetic resonance imaging(MRI)and nuclear magnetic resonance(NMR)studies.The equations deal with uncoupled(-1/2)spins associated with three-dimensional spatial dynamics represented by diffusion and flow.The proposed method recommends using an unopened Kronecker product for evolution generators to minimize the simulation time and reduce the occupied computer memory.Two and three-dimensional diffusionweighted magnetic resonance imaging associated with four pairs of coupled spin systems were utilized to achieve the study's goals.Utilizing four pairs of coupled spin systems in MRI simulation enhances accuracy and realism in modeling interactions between spins,leading to improved tissue characterization and diagnostic capabilities.The obtained results were impossible using previous simulation packages.The results of the study demonstrate that the Spinach library can simulate complex spin systems with significant spatial dynamics.展开更多
文摘Let <i>f</i>(u) and <i>g</i>(v) be two polynomials of degree <i>k</i> and <i>l</i> respectively, not both linear which split into distinct linear factors over F<sub>q</sub>. Let <img src="Edit_83041428-d8b0-4505-8c3c-5e29f2886159.png" width="160" height="15" alt="" /> be a finite commutative non-chain ring. In this paper, we study polyadic codes and their extensions over the ring <i>R</i>. We give examples of some polyadic codes which are optimal with respect to Griesmer type bound for rings. A Gray map is defined from <img src="Edit_c75f119d-3176-4a71-a36a-354955044c09.png" width="50" height="15" alt="" /> which preserves duality. The Gray images of polyadic codes and their extensions over the ring <i>R</i> lead to construction of self-dual, isodual, self-orthogonal and complementary dual (LCD) codes over F<i><sub>q</sub></i>. Some examples are also given to illustrate this.
文摘The architectural development of Acacia karroo conforms to Troll’s model. Growth of the branches is modular and sympodial with heteroblastic leaves on all long shoots of the tree, including the seedling. Axillary buds tend to proliferate especially on flowering shoots where they form fascicles consisting of up to 10 inflorescences arranged in two parallel serial rows per leaf axil. Most axillary buds are sylleptic and basal buds which give rise to short shoots, each producing two to five cataphylls each season, but no flowers. Inflorescences are only produced on long shoots (modules) of the current season. After flowering the terminal part of the module aborts, trees are usually andromonoecious with capitate inflorescences containing 40 to 100 flowers each, with some male and some hermaphrodite. Some trees produce only male flowers. Anthesis in the same inflorescence, the same tree as well as amongst trees of the same community are synchronised and occur at intermittent intervals, each lasting three or more days at a time. Flowers are protogynous and pollen is produced in polyads, each consisting of 16 pollen grains. Ovaries contain 10 to 14 ovules each. The concave stigma has space for only one polyad which can fertilise all ovules in the ovary after a single pollination event. Fruit set is low with 0 to 10 fruits (pods) per inflorescence.
文摘Modern magnetic resonance imaging(MRI)experiments require simultaneous spin and spatial dynamics treatment.This paper aims to demonstrate the possibility of simulating a large spin system for diffusion-weighted MRI experiments.The numerical simulation of diffusion MRI depends on Bloch-Torrey equations.The latter describe the behavior of spin systems under the influence of magnetic fields and diffusion processes.They are particularly relevant in magnetic resonance imaging(MRI)and nuclear magnetic resonance(NMR)studies.The equations deal with uncoupled(-1/2)spins associated with three-dimensional spatial dynamics represented by diffusion and flow.The proposed method recommends using an unopened Kronecker product for evolution generators to minimize the simulation time and reduce the occupied computer memory.Two and three-dimensional diffusionweighted magnetic resonance imaging associated with four pairs of coupled spin systems were utilized to achieve the study's goals.Utilizing four pairs of coupled spin systems in MRI simulation enhances accuracy and realism in modeling interactions between spins,leading to improved tissue characterization and diagnostic capabilities.The obtained results were impossible using previous simulation packages.The results of the study demonstrate that the Spinach library can simulate complex spin systems with significant spatial dynamics.
