Here quantum theory representations of real (R) and complex (C) numbers are described as equivalence classes of Cauchy sequences of states of single, finite strings of qukits where the qukit string states represent rational numbers. This work extends earlier work with qubit string states to qukit string states for any base k ≥ 2. Quantum theory representations differ from the usual classical re...

let be a locally compact non?abelian group and be a compact subgroup of also let be a ?invariant measure on the homogeneous space . in this article, we extend the linear operator as a bounded surjective linear operator for all ?spaces with . as an application of this extension, we show that each frame for determines a frame for and each frame for arises from a frame in via the linear operator .

The simplest bimodal combination of unimodal logics L1 and L2 is their fusion, L1 ⊗ L2, axiomatized by the theorems of L1 for 1 and of L2 for 2, and the rules of modus ponens, substitution and necessitation for 1 and for 2. Shehtman introduced the frame product L1 × L2, as the logic of the products of certain Kripke frames: these logics are two-dimensional as well as bimodal. Van Benthem, Bezha...

Adding steel braces to reinforced concrete frames is a common way for seismic rehabilitation of these structures. Due to ease of installation and the possibility of creating openings in the braced bays, this method of rehabilitation has been more preferred than using shear walls. In this paper, three experimental specimens including a reinforced concrete frame, a reinforced concrete frame with ...

The existence of nonannotated protein-coding human short open reading frames (sORFs) has been revealed through the direct detection of their sORF-encoded polypeptide (SEP) products. The discovery of novel SEPs increases the size of the genome and the proteome and provides insights into the molecular biology of mammalian cells, such as the prevalent usage of nonAUG start codons. Through modifica...

In this paper, a novel approach for detection of text and non-text regions in video frames is proposed. The proposed approach performs block wise eigen analysis on the gradient image of the video frame. For each block of the gradient frame, the dominant eigen value is computed to decide if the block could be a candidate text block. The K-means clustering is then applied to further identify text...

In this paper, a new method to model ECG signals by means of "Predefined Personalized Signature and Envelope Functions" is presented. ECG signals are somewhat unique to a person. Moreover, it presents quasi-stationary behavior. Therefore in this work, on a frame basis, personal ECG signals Xi(t) is modeled by the form of Xi(t) ≈ Ciφi(t) αi(t). In this model, φi(t) is defined as the Personalized...

We construct light cones for the semi-analytic galaxy formation simulation of Guo et al. and make mock catalogues for comparison with deep high-redshift surveys. Photometric properties are calculated with two different stellar population synthesis codes in order to study sensitivity to this aspect of the modelling. The catalogues are publicly available and include photometry for a large number ...

The subset X0 = [sequence: see text] of 20 trinucleotides has a preferential occurrence in frame 0 (a reading frame established by the ATG start trinucleotide) of protein (coding) genes of both prokaryotes and eukaryotes. This subset X0++ has the rarity property (6 x 10(-8)) to be a complementary maximal circular code with two permutated maximal circular codes X1 and X2 in frames 1 and 2 respec...

Abstract We settle a part of the conjecture by Bandini and Valentino [‘On structure slopes Drinfeld cusp forms’, Exp. Math. 31 (2) (2022), 637–651] for $S_{k,l}(\Gamma _0(T))$ when $\mathrm {dim}\ S_{k,l}(\mathrm {GL}_2(A))\leq 2$ . frame check primes $\mathfrak {p}$ higher levels {p}\mathfrak {m}$ , show that level {p} \mathfrak does not hold if {m}\ne A$ $(k,l)=(2,1)$