The Optimization of PCI Interference in the 4G LTE Network in Padang

With the growth of the customers and the expansion of the 4G LTE network in the area of Padang City, a PCI (Physical cell identity) modulo interference spot has been detected. PCI modulo interference occurs when an area is covered by two or more cells, which have a strong signal, and these cells have the same PCI modulo value. Based on the measurement results by the driving test method, the network conditions were not optimal because the SINR percentage (Signal to Interference Noise Ratio) in the good category was still low, at 9.47%, and the download throughput in the good category was 18.94%. This indicated that the interference in the area was quite high. Thus, it was necessary to do optimization action. The optimization action was taken by rotating the PCI on the site by considering the modulo value of each site so that the PCI with the same modulo did not merely lead to one location. Besides, action was taken to change the azimuth direction of cells that were too dominant. Based on the optimization process that has been carried out and the driving test activities that have been carried out again, the performance in the existing conditions has increased. The SINR percentage in the good category increased by 10%, so it became 19.47%, and the download throughput in the good category increased by 44.74% and became 63.68%.

Equations in oligomorphic clones and the constraint satisfaction problem for ω-categorical structures

There exist two conjectures for constraint satisfaction problems (CSPs) of reducts of finitely bounded homogeneous structures: the first one states that tractability of the CSP of such a structure is, when the structure is a model-complete core, equivalent to its polymorphism clone satisfying a certain nontrivial linear identity modulo outer embeddings. The second conjecture, challenging the approach via model-complete cores by reflections, states that tractability is equivalent to the linear identities (without outer embeddings) satisfied by its polymorphisms clone, together with the natural uniformity on it, being nontrivial. We prove that the identities satisfied in the polymorphism clone of a structure allow for conclusions about the orbit growth of its automorphism group, and apply this to show that the two conjectures are equivalent. We contrast this with a counterexample showing that [Formula: see text]-categoricity alone is insufficient to imply the equivalence of the two conditions above in a model-complete core. Taking another approach, we then show how the Ramsey property of a homogeneous structure can be utilized for obtaining a similar equivalence under different conditions. We then prove that any polymorphism of sufficiently large arity which is totally symmetric modulo outer embeddings of a finitely bounded structure can be turned into a nontrivial system of linear identities, and obtain nontrivial linear identities for all tractable cases of reducts of the rational order, the random graph, and the random poset. Finally, we provide a new and short proof, in the language of monoids, of the theorem stating that every [Formula: see text]-categorical structure is homomorphically equivalent to a model-complete core.

Duality and the existence of weakly completely continuous elements in aB*-algebra

Ogasawara and Yoshinaga [9] have shown that aB*-algebra is weakly completely continuous (w.c.c.) if and only if it is*-isomorphic to theB*(∞)-sum of algebrasLC(HX), where eachLC(HX)is the algebra of all compact linear operators on the Hilbert spaceHx.As Kaplansky [5] has shown that aB*-algebra isB*-isomorphic to theB*(∞)-sum of algebrasLC(HX)if and only if it is dual, it follows that a5*-algebraAis w.c.c. if and only if it is dual. We have observed that, if only certain key elements of aB*-algebraAare w.c.c, thenAis already dual. This observation constitutes our main theorem which goes as follows.A B*-algebraAis dual if and only if for every maximal modular left idealMthere exists aright identity modulo M that isw.c.c.

On Semigroups of Transformations Acting Transitively on a Set

We call a semigroup S transitive if S is isomorphic to a semigroup T of transformations of some set M into itself, where T acts on M transitively, that is in such a manner that for all x, y ∊ M we have Xπ = y for some transformation π∊T. In [4] the author showed that S is transitive if and only if there exists a right congruence σ (i.e., an equivalence relation for which a σ b always implies ac σ bc for all c ∊ S) on S, satisfying:(1)There exists a left identity modulo σ, that is an element e such that ea σ a for all a ∊ S .(2)Each σ-class meets each right ideal, or, equivalently, for all a, b ∊ S we have ac σ b for some c ∊ S .(3)The relation σ contains ( i. e. , is less fine than) no left congruence except the identity relation (in which each class consists of a single element).