A variant of the Hardy-Ramanujan theorem

For each natural number $n$, we define $\omega^*(n)$ to be the number of primes $p$ such that $p-1$ divides $n$. We show that in contrast to the Hardy-Ramanujan theorem which asserts that the number $\omega(n)$ of prime divisors of $n$ has a normal order $\log\log n$, the function $\omega^*(n)$ does not have a normal order. We conjecture that for some positive constant $C$, $$\sum_{n\leq x} \omega^*(n)^2 \sim Cx(\log x). $$ Another conjecture related to this function emerges, which seems to be of independent interest. More precisely, we conjecture that for some constant $C>0$, as $x\to \infty$, $$\sum_{[p-1,q-1]\leq x} {1 \over [p-1, q-1]} \sim C \log x, $$ where the summation is over primes $p,q\leq x$ such that the least common multiple $[p-1,q-1]$ is less than or equal to $x$.

Dynamics of the Cavity Radiation of a Correlated Emis-sion Laser Coupled to a Two-Mode Thermal Reservoir

In this paper, the quantum properties of the cavity light beam produced by a coherently driven nondegenerate three-level laser with an open cavity and coupled to a two-mode thermal reservoir are thoroughly analyzed. We have carried out our analysis by putting the noise operators associated with the thermal reservoir in normal order. Here we discussed more the effect of thermal light and the spontaneous emission on the dynamics of the quantum processes. It is found that the maximum degree of intracavity squeezing 43% below the vacuum-state level. Moreover, the presence of thermal light leads to decrease the degree of entanglement.

Reopening of Surabaya Zoo in Coronavirus Disease 2019 (Covid-19) Pandemic

High spread of Covid-19 in Surabaya implemented on a Large-Scale Social Restrictions policy. This has impacted on closure of tourist destinations, including Surabaya Zoo. During the closing period, Surabaya Zoo suffered significant losses due to the absence of revenue that impacted on the conservation operations in saving endangered animals. Based on Surabaya Mayor Regulation of New Normal Order Guidelines Number 28 of 2020 as amended by Number 33 of 2020, Surabaya Zoo is reopened. This fact is an interesting issue to study how well the management in handling this situation. The writing method used in this paper is a literature review and primary data collection as a form of best practice that might be adopted in Surabaya Zoo. The results showed that management is succeeded in reopening Surabaya Zoo. The conclusion from this study is Surabaya Zoo is recommended to be reopened during the first stage of New Normal

IMPLEMENTASI KEBIJAKAN BELAJAR DARI RUMAH DENGAN TATANAN NORMAL BARU PADA SEKOLAH DASAR DI KECAMATAN BULAK KOTA SURABAYA

The spread of COVID-19 in Indonesia is increasing every day. urged the government to immediately deal with the COVID-19 pandemic by making various policies such as implementing a lockdown, social distancing, physical distancing, self-isolation and Large-Scale Social Restrictions (PSBB). With this government policy, it certainly has a big impact in various aspects of life, especially in the aspect of education in Indonesia. With the implementation of PSBB, it encourages the government to issue policies on the implementation of education in Indonesia, because after all the learning process must continue so that the objectives of education can be achieved as a whole. The purpose of this study is to describe the implementation of learning from home policies with the new normal order in elementary schools in Bulak District, Surabaya City. The theory used in this research is the theory of implementation model by Edward III. This type of research uses descriptive qualitative. The results of this study indicate that: (1) Communication has been implemented well; (2) Resources are well implemented but staff are not sufficient; (3) The disposition has been implemented very well; (4) The bureaucratic structure is well implemented.

Microscopic Image Retrieval Scheme Using Neural Network For Multi Image Queries

In this paper, we describe the plan and advancement of a neural network based image retrieval framework for microscopic images using a reference information base that contains images of more than one information. Such an extraction requires a point by point assessment of retrieval execution of image highlights. This paper presents a survey of crucial parts of content based image retrieval including highlight extraction of color and surface highlights. The proposed neural network based image retrieval framework utilizes a multitier way to deal with arrange and recover microscopic images including their particular subtypes, which are generally hard to separate and characterize. Broad examinations on neural network based image retrieval frameworks show that low-level image highlights can't generally depict elevated level semantic ideas in the clients mind. This framework empowers multi-image inquiry to ensure the semantic consistency among the recovered images. New weighting terms, roused from information retrieval hypothesis, are characterized for multiple-image inquiry and retrieval. The multi-image inquiry calculation with the proposed weighting technique accomplishes about normal order exactness at the main position retrieval, beating the image-level retrieval precision by about ideal rate focuses for different infections separately. Utilizing low level highlights just does exclude human insight. In the event that human mediation is permitted in the image retrieval framework the proficiency supports up.

Comparison of Discrete Fourier Transform and Fast Fourier Transform with Reduced Number of Multiplication and Addition Operations

Fast Fourier Transform is an advanced algorithm for computing Discrete Fourier Transform efficiently. Although the results available from the operation of Discrete Fourier Transform (DFT) and Fast Fourier Transform (FFT) are same, but exploiting the periodicity and symmetry property of phase factor Fast Fourier Transform computes the Discrete Fourier Transform using reduced number of multiplication and addition operations. The basic structure used in the operations of Fast Fourier Transform is the Butterfly structure. For the implementation of Fast Fourier Transform the two methods are used such as decimation in time (DIT) and decimation in frequency (DIF). Both the methods give same result but for decimation in time of Fast Fourier Transform bit reversed inputs are applied and for decimation in frequency of Fast Fourier Transform normal order inputs are applied, and the result is reversed again. In this paper, operations for DFT and FFT have been discussed and shown with examples. It is found that generalized formula for FFT have been described same in the books, but the expressions in the intermediate computations for the first decimation and second decimation are different in the various books of Digital Signal Processing. The expressions in the intermediate computation of FFT described in different books are broadly compared in this paper

I–Convergence of Arithmetical Functions

Let n > 1 be an integer with its canonical representation, n = p 1 α 1 p 2 α 2 ⋯ p k α k . Put H n = max α 1 … α k , h n = min α 1 … α k , ω n = k , Ω n = α 1 + ⋯ + α k , f n = ∏ d ∣ n d and f ∗ n = f n n . Many authors deal with the statistical convergence of these arithmetical functions. For instance, the notion of normal order is defined by means of statistical convergence. The statistical convergence is equivalent with I d –convergence, where I d is the ideal of all subsets of positive integers having the asymptotic density zero. In this part, we will study I –convergence of the well-known arithmetical functions, where I = I c q = A ⊂ N : ∑ a ∈ A a − q < + ∞ is an admissible ideal on N such that for q ∈ 0 1 we have I c q ⊊ I d , thus I c q –convergence is stronger than the statistical convergence ( I d –convergence).

Uncommon Divisions

At times one finds Galant expositions that are framed by punctuation sequences of types not specifically cited by Heinrich Christoph Koch. These include punctuation sequences that involve (1) resting points over less typical harmonies, such as a submediant or subdominant triad; (2) successive, contrasting Absätze that lead to the same type of resting point; and (3) standard resting points that appear out of their normal order. Some of these layouts nonetheless may be understood as stylistic generic (if somewhat less common) options. In other instances, however, these unusual punctuation sequences are best understood as expressive deviations that are in dialog with more conventional successions of expositional resting points.