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We theoretically explore the properties of heralded number states including up to three photons that are generated from single-mode twin beams. We investigate the effects of different parameters involved in the state preparation by using the fidelity, normalized second-order factorial moment of photon number for the heralded state ( g h ( 2 ) ) , and photon-number parity as figures of merit. Especially, the photon-number parity offers a practical and robust tool for inferring the target state quality by capturing the contamination of all undesired photon-number contributions. We focus on expressing our results in terms of experimentally easily accessible parameters such as the coincidences-to-accidentals ratio and the detection efficiencies. Our results identify the optimal parameter regions for generating high quality photon-number states by heralding and provide useful insights for advancing their use in quantum technologies.

Due to their strict photon-number correlation, the twin beams produced in parametric down-conversion (PDC) work well for heralded state generation. Often, however, this state manipulation is distorted by the optical losses in the herald and by the higher photon-number contributions inevitable in the PDC process. In order to find feasible figures of merit for characterizing the heralded states, we investigate their normalized factorial moments of the photon number that can be accessed regardless of the optical losses in the detection. We then perform a measurement of the joint photon statistics of twin beams from a semiconductor Bragg-reflection waveguide with transition-edge sensors acting as photon-number-resolving detectors. We extract the photon-number parity of heralded single photons in a loss-tolerant fashion by utilizing the moment generating function. The photon-number parity is highly practicable in quantum state characterization, since it takes into account the complete photon-number content of the target state.

An iterated tower of number fields is constructed by adding preimages of a base point by iterations of a rational map. A certain basic quadratic rational map defined over the Gaussian number field yields such a tower of which any two steps are relative bicyclic biquadratic extensions. Regarding such towers as analogues of [Z.sub.2]-extensions, we examine the parity of 2-ideal class numbers along the towers with some examples. Key words: Iterated extension; class number parity; Iwasawa theory.

Fully Homomorphic Encryption (FHE) permits processing information in the form of ciphertexts without decryption. It can ensure the security of information in common technologies used today, such as cloud computing, the Internet of Things, and machine learning, among others. A primary disadvantage for its practical application is the low efficiency of sign and comparison operations. Several FHE schemes use the Residue Number System (RNS) to decrease the time complexity of these operations. Converting from the RNS to the positional number system and calculating the positional characteristic of a number are standard approaches for both operations in the RNS domain. In this paper, we propose a new method for comparing numbers and determining the sign of a number in RNS. We focus on the even ranges that are computationally simple due to their peculiarities. We compare the performance of several state-of-art algorithms based on an implementation in C++ and relatively simple moduli with a bit depth from 24 to 64 bits. The experimental analysis shows a better performance of our approach for all the test cases; it improves the sign detection between 1.93 and 15.3 times and the number comparison within 1.55–11.35 times with respect to all the methods and configurations.

The present study was designed to assess the impact of husbandry, stage of lactation and parity number on milk yield and chemical composition of camel milk within three different camel farms at Khartoum State, Sudan. Camel milk samples were collected from 43 healthy she-camels at different lactation stages and parity number. The overall means of daily milk yield and composition of fat, protein, lactose, solids not fat, acidity and density were 2.73±1.16 L/day, 3.69±1.31%, 3.32±0.33%, 4.59±0.45, 8.49±0.86%, 0.19±0.03% and 1.030±0.017g/cm3, respectively. Camel milk yield and composition were significantly affected by husbandry, stage of lactation and parity number. The highest milk yield was recorded for she-camels kept in the intensive farming system during early stage of lactation. This study concluded that husbandry systems, stage of lactation and parity number have impact on milk yield and chemical composition of camel milk. Therefore, factors that cause variations in milk yield and composition should be considered for the nutritional and technological uses of camel milk.

The parities of ideal class numbers of compositum of quadratic function fields are studied. Especially, the parities of ideal class numbers of are completely determined in detail, where are monic irreducible polynomials of even degrees.

The aim of this study was to analyze the effect of season and number of parity on the reproductive performance of sows kept on a commercial farm. To achieve this objective, 800 nrs productive parent sows and a total of 958 parities were analyzed. The results show that sow’s breeding season had a significant effect on the weaning-to-oestrus interval, the farrowing rate, the litter size and weaning piglets with positive results during autumn, winter and spring seasons. The number of parity has a significant effect on the weaning-to-oestrus interval, litter size and weaning piglets with acceptable values in sows with more farrowing. The results of this study on a pig farm with analysis which highlights the risk factors associated with reproductive performance of sows, could be used to improve sow farm practices.

BACKGROUND AND AIM: One of the major public health problems in Turkey is the high prevalence of obesity, which is particularly frequent among women. As it has been reported that parity affects body fat and BMI, the aim of this study was to evaluate the association between parity number, socioeconomic status and obesity. SUBJECTS AND METHODS: The study involved 286 married or divorced women aged 28- 80 years (mean age: 46.7±9.7), who were divided into two groups depending on whether they had experienced three or fewer pregnancies (group 1) or four or more pregnancies (group 2). We measured their body weight and height, and waist and hip circumferences, calculated their BMI, and determined their body fat percentage and fat mass by means of bioelectric impedance. RESULTS: The women in group 2 had a higher BMI, a greater fat percentage and fat mass, a larger waist circumference and higher waist/hip ratio values than those in group 1, and their mean age and illiteracy ratio were also higher. There was a significant correlation between parity number and body weight, BMI and hip circumference. CONCLUSIONS: Among other risk factors, a high parity number and socioeconomic indices may be associated with obesity in women.

Graph Theory A strong parity vertex coloring of a 2-connected plane graph is a coloring of the vertices such that every face is incident with zero or an odd number of vertices of each color. We prove that every 2-connected loopless plane graph has a strong parity vertex coloring with 97 colors. Moreover the coloring we construct is proper. This proves a conjecture of Czap and Jendrol' [Discuss. Math. Graph Theory 29 (2009), pp. 521-543.]. We also provide examples showing that eight colors may be necessary (ten when restricted to proper colorings).

The objective of this study was to determine the effect of some factors on the length of productive life (LPL), the number of parities (NP), and the culling interval (CI) of sows. The information from 2003 to 2009 of 3,746 sows with LPL and NP records and 5,819 sows with CI records from the four farms of Yucatan, Mexico was used. LPL was defined as the number of days between the first farrowing and culling or death and CI as the number of days between the last farrowing and culling. To determine the effects of farm, litter size at first farrowing (LSF1) and age at first farrowing (AF1) on LPL and NP, and of farm, LSF1 and culling reason on CI general linear models were used. Means and standard errors for LPL, NP, and CI were 496.4 ± 8.42 days, 3.35 ± 0.04 parities, and 48.3 ± 0.52 days, respectively. All factors had significant effects ( P  < 0.05) on LPL, NP, and CI. The sows from farm 2 stayed longer (806.0 days) and had more parities (5.25) than the sows from the other farms. Sows with the smallest litters (≤8 piglets) at first farrowing stayed the least time in the farm (675.1 days) and had the fewest parities (4.49). Gilts farrowing the first time before 331 days of age stayed longer time in the farm (726.4 days) and had more parities (4.81) in comparison with 331–348 and more than 348 days age groups. With respect to CI, the sows in farm 3 stayed the longest time in the farm. Sows with more than five parities were culled sooner after their last farrowing. In conclusion, differences between farms for LPL, PN, and CI were found. Females that farrowed at a short age and those with large litters stayed longer in the herd. Old sows and those culled for reproductive reasons stayed the least time in the herd after their last farrowing.