Evaluation of a Product Derived from Porcine Plasma Protein and a Yeast Product with Similar Biological Activity in Diets of Growing Broilers

The post-hatch period of a broiler is an integral point in their development and for the programming of musculoskeletal and immune cells. Therefore, the efficacy of two bioactive protein products, betaGRO® (BG) and celluTEIN® (CT) to impact post-hatch and lifelong development was evaluated. Birds were grown under a low stress environment using clean wood shavings litter and a high stress environment with used litter from a commercial farm that had suffered high mortality. Each additive was fed at 300 g/ton from day 1–14 and 50 g/ton from day 15–42. Growing birds in the high stress environment had a negative impact on performance (p < 0.05); however, addition of either BG or CT successfully mitigated the detriments of the high stress environment (p < 0.05), and in many cases, the performance was equal to or better than the performance of birds on the control diet in the low stress environment. Birds fed BG and CT experienced improvements in 42-day feed conversion, and were more uniform than birds grown consuming the control diet (p < 0.05). Mortality of birds in the high stress environment was reduced by addition of BG or CT (p < 0.05). Addition of BG and CT resulted in improvements in carcass and breast meat yield (p < 0.05). Together, these data suggest that BG and CT can be used interchangeably to improve broiler health and performance.

Inverse Derivative Operator and Umbral Methods for the Harmonic Numbers and Telescopic Series Study

The formalism of differ-integral calculus, initially developed to treat differential operators of fractional order, realizes a complete symmetry between differential and integral operators. This possibility has opened new and interesting scenarios, once extended to positive and negative order derivatives. The associated rules offer an elegant, yet powerful, tool to deal with integral operators, viewed as derivatives of order-1. Although it is well known that the integration is the inverse of the derivative operation, the aforementioned rules offer a new mean to obtain either an explicit iteration of the integration by parts or a general formula to obtain the primitive of any infinitely differentiable function. We show that the method provides an unexpected link with generalized telescoping series, yields new useful tools for the relevant treatment, and allows a practically unexhausted tool to derive identities involving harmonic numbers and the associated generalized forms. It is eventually shown that embedding the differ-integral point of view with techniques of umbral algebraic nature offers a new insight into, and the possibility of, establishing a new and more powerful formalism.

Sacral Heritage of the Carpathian Region and Management of its Resource Component in Tourism Activity

The Carpathian Recreation/Tourism Region (hereafter – CRTR) in Ukraine is a unique territory featuring the sacral historic-cultural heritage of different-time periods beginning from Ancient Rus, Lithuanian, Ottoman, Austro-Hungarian and until Polish, Ro- manian, Czech and Ukrainian times. This is why it seems urgently necessary to assess in as much detail as possible the sacral historic-cultural heritage (hereafter – HCH) of the Carpathian Recreation/Tourism Region in Ukraine and provide for the mechanisms of management of the same so that the aforementioned heritage will be as quickly and intensely as possible involved into a common cultural and tourism space and trans-border cooperation with neighboring EU countries, that is, Ro- mania, Slovakia, Poland, Hungary and Moldova. For this purpose different types of conservation status (e.g., UNESCO and national heritage) were considered and spatial differences in the sacral historic-cultural monuments (hereafter – HCM) were analyzed through the assessment of their number, modified indices of the sacral objects’ concentration, coefficients of localization and educational value, etc, with application of the methods of partial and integral point-based ranking and cluster analysis with respect to the 58 administrative districts of the region. Following the survey of the CRTR where the sacral HCM were found to be the range from average to very good condition , and proceeding from ethnographic-historical context, the region was spatially differentiated into the Roztotsko-Boykivskyy Meso-District on the northwest, the Hutsul Meso-District in the Prykarpattia, and the Bukovynian Ukrainian-speaking and Romanian- speaking micro-districts in the Prypruttia. Among the 6 formed district-status CRTR clusters, 3 of them (27.6% of the administrative districts of the region) were assessed as the most optimal for the purpose of efficient tourism/excursion activity (hereafter - TEA) and its management, while average geometric indices of all aforesaid coefficients ranged from the above-average (4.10) to the highest (7.59) throughout the whole region. It is suggested to achieve efficient tourism management within the studied territories by way of more active introduction of a series of previously tested pilgrimages and educative-religious tours, as well as through different interstate events of trans-border cooperation. All these would increase the competitiveness of the HCM-oriented tourism industry, be helpful in ascertaining which specifically attractive territories should receive investment, and help integrate the Carpathian Region of Ukraine into the common cultural and tourism space of the EU countries.

Comparative analysis of efficiency of democracy in Ukraine according to the indices of democracy The Economist Democracy Index, Freedom In the World and Polity IV

This article represents an analysis of efficiency of Ukrainian democracy within the framework of three popural indices of democracy – The Economist Democracy Index, Freedom In the World index and Polity IV. Comparative analysis shows the core factors which bring three different democratic concepts, used in the indices, to the integral unity. Finding correlation between factors of Ukrainian democracy, measured in the indices through a certain time period (2006-2018), helps getting integral look at the problem of non existent universal theoretic base for understanding democracy. The basic idea of the analysis, represented in this article, shows that different factors, used by indices in measuring democracy, do not evenly correlate in practice, though they represent holistic approach to the essence of democracy. Choosing specific theoretical approach of understanding democracy makes it hard for indices to fully measure real democracy. This analysis aims at searching correlation in different basic factors of democratic models, used by indices with different approaches. As the result of the analysis the article ranks a number of basic factors, used in three popular indices of democracy, according to the strength of correlation of these factors with other factors of the index they represent and with the final score of the index. Integral choice of the basic factors, which correlate with the change of Ukraine’s democratic trends according to the three indices, covers several dimensions of democratic model. Ukrainian democratic trends in the specific time period (2006-2018), as the analysis shows, from integral point of view correlates the most with the changes in electoral process and pluralism, civil liberties and legal restrictions of the executive power. Political culture, political participation and individual rights show weak correlation with Ukrainian democratic trends within the period of time, chosen for the analysis.

Study on the Manifold Cover Lagrangian Integral Point Method Based on Barycentric Interpolation

To achieve numerical simulation of large deformation evolution processes in underground engineering, the barycentric interpolation test function is established in this paper based on the manifold cover idea. A large-deformation numerical simulation method is proposed by the double discrete method with the fixed Euler background mesh and moving material points, with discontinuous damage processes implemented by continuous simulation. The material particles are also the integration points. This method is called the manifold cover Lagrangian integral point method based on barycentric interpolation. The method uses the Euler mesh as the background integral mesh and describes the deformation behavior of macroscopic objects through the motion of particles between meshes. Therefore, this method can avoid the problem of computation termination caused by the distortion of the mesh in the calculation process. In addition, this method can keep material particles moving without limits in the set region, which makes it suitable for simulating large deformation and collapse problems in geotechnical engineering. Taking a typical slope as an example, the results of a slope slip surface obtained using the manifold cover Lagrangian integral point method based on barycentric interpolation proposed in this paper were basically consistent with the theoretical analytical method. Hence, the correctness of the method was verified. The method was then applied for simulating the collapse process of the side slope, thereby confirming the feasibility of the method for computing large deformations.

Mapping Technology Based Tools of Audience Engagement

In order to survive or adapt to new tendencies, cultural organisations must enhance audience engagement. This article proposes a new look at the concept of audience engagement from an integral point of view evaluating and analysing it by means of the conception of a map. The prototype of mapping audience engagement tools created in this article can help cultural organisations to effectively measure and evaluate actions in order to coordinate and select effective audience engagement tools. The empirical part of the article introduces a study of 18 Kaunas City (Lithuania) cultural organisations which reveals that organisations mostly focus on online activities, especially in the categories of accessibility and cognition, and there is a lack of collective development and more active audience engagement in programme development as well as promotion of discussions and original additional context.

ON INTEGRAL POINTS ON ISOTRIVIAL ELLIPTIC CURVES OVER FUNCTION FIELDS

Let $k$ be a finite field and $L$ be the function field of a curve $C/k$ of genus $g\geq 1$. In the first part of this note we show that the number of separable $S$-integral points on a constant elliptic curve $E/L$ is bounded solely in terms of $g$ and the size of $S$. In the second part we assume that $L$ is the function field of a hyperelliptic curve $C_{A}:s^{2}=A(t)$, where $A(t)$ is a square-free $k$-polynomial of odd degree. If $\infty$ is the place of $L$ associated to the point at infinity of $C_{A}$, then we prove that the set of separable $\{\infty \}$-points can be bounded solely in terms of $g$ and does not depend on the Mordell–Weil group $E(L)$. This is done by bounding the number of separable integral points over $k(t)$ on elliptic curves of the form $E_{A}:A(t)y^{2}=f(x)$, where $f(x)$ is a polynomial over $k$. Additionally, we show that, under an extra condition on $A(t)$, the existence of a separable integral point of ‘small’ height on the elliptic curve $E_{A}/k(t)$ determines the isomorphism class of the elliptic curve $y^{2}=f(x)$.

The positive integral points on the elliptic curve 𝒚𝟐=𝟕𝒑𝒙(𝒙𝟐+𝟖)

The integral point of elliptic curve is a very important problem in both elementary number theory and analytic number theory. In recent years, scholars have paid great attention to solving the problem of positive integer points on elliptic curve 𝑦2 = 𝑘(𝑎𝑥2+𝑏𝑥+𝑐), where 𝑘,𝑎,𝑏,𝑐 are integers. As a special case of 𝑦2 = 𝑘(𝑎𝑥2+𝑏𝑥+𝑐), when 𝑎 = 1,𝑏 = 0,𝑐 = 22𝑡−1, it turns into 𝑦2 = 𝑘𝑥(𝑥2+22𝑡−1), which is a very important case. However ,at present, there are only a few conclusions on it, and the conclusions mainly concentrated on the case of 𝑡 = 1,2,3,4. The case of 𝑡 = 1, main conclusions reference [1] to [7]. The case of 𝑡 = 2, main conclusions reference [8]. The case of 𝑡 = 3, main conclusions reference [9] to [11]. The case of 𝑡 = 4, main conclusions reference [12] and [13]. Up to now, there is no relevant result on the case of 𝑘 = 7𝑝 when 𝑡 = 2, here the elliptic curve is 𝑦2 = 7𝑝(𝑥2 + 8), this paper mainly discusses the positive integral points of it. And we obtained the conclusion of the positive integral points on the elliptic curve 𝑦2 = 7𝑝(𝑥2 + 8). By using congruence, Legendre symbol and other elementary methods, it is proved that the elliptic curve in the title has at most one integer point when 𝑝 ≡ 5,7(𝑚𝑜𝑑8).