Relations in the Size Variation of Plant Organs: a Case Study of Staghorn Sumac Leaves and Longleaf Pine Cone Scales

Plants automatically control the size variations in organs to achieve efficient exploitation of resources. However, it is unclear whether the scaling relationships of plant organs share a similar character for different individuals under varied micro-conditions (e.g., light and soil water). We conducted a case study of the lengths of staghorn sumac leaves and longleaf pine cone scales to test the relationships. Our results indicated that although there were size variations, there existed power laws of frequency in the lengths of staghorn sumac leaves and longleaf pine cone scales. The exponents differed but were positively correlated with the minimum length of leaves or cone scales. Taylor’s Law existed in the lengths of cone scales and some tree leaves, and scale break was observed. This study provides new information on scaling relationships and self-organization in the patterns of tree parts arrangement. Taylor’s Law may be used to detect minor changes in the growth regime.

On cutting blocking sets and their codes

Let PG ⁡ ( r , q ) {\operatorname{PG}(r,q)} be the r-dimensional projective space over the finite field GF ⁡ ( q ) {\operatorname{GF}(q)} . A set 𝒳 {\mathcal{X}} of points of PG ⁡ ( r , q ) {\operatorname{PG}(r,q)} is a cutting blocking set if for each hyperplane Π of PG ⁡ ( r , q ) {\operatorname{PG}(r,q)} the set Π ∩ 𝒳 {\Pi\cap\mathcal{X}} spans Π. Cutting blocking sets give rise to saturating sets and minimal linear codes, and those having size as small as possible are of particular interest. We observe that from a cutting blocking set obtained in [20], by using a set of pairwise disjoint lines, there arises a minimal linear code whose length grows linearly with respect to its dimension. We also provide two distinct constructions: a cutting blocking set of PG ⁡ ( 3 , q 3 ) {\operatorname{PG}(3,q^{3})} of size 3 ⁢ ( q + 1 ) ⁢ ( q 2 + 1 ) {3(q+1)(q^{2}+1)} as a union of three pairwise disjoint q-order subgeometries, and a cutting blocking set of PG ⁡ ( 5 , q ) {\operatorname{PG}(5,q)} of size 7 ⁢ ( q + 1 ) {7(q+1)} from seven lines of a Desarguesian line spread of PG ⁡ ( 5 , q ) {\operatorname{PG}(5,q)} . In both cases, the cutting blocking sets obtained are smaller than the known ones. As a byproduct, we further improve on the upper bound of the smallest size of certain saturating sets and on the minimum length of a minimal q-ary linear code having dimension 4 and 6.

Principles of Construction and Mathematical Models of the Formation of a Solidarity Fund in an Alternative Old-Age Pension System

The basic principles of the formation of a solidary fund in the suggested old-age pension system are to establish the minimum length of service according to which a citizen has the right to an old-age pension, the implementation into the pension calculation system of the indicator "share deducted to a solidary fund" from each transfer to the personal account of the employee, so that by retirement at the age of 60 and working experience of 38 years, the pension amount was exactly equal to the amount of wages used in calculations. With a decrease in the length of service, the pension amount is reduced according to a certain rule. To implement these principles, appropriate mathematical models have been built that allow to calculate the amount of accumulated pension capital, own pension, accumulated amounts in the solidary fund, the total amount in the pension fund, etc., with any work experience, the amount of wages. Complex calculations were performed using the parameters that have developed in the practice of today. The results of the calculations are presented in tables with the corresponding comments.

Một số cải tiến cho các kiểm tra thống kê tính ngẫu nhiên sử dụng so khớp mẫu

Tóm tắt—Các kiểm tra liên quan đến so khớp mẫu chồng lấp đã được đề xuất trong NIST SP 800-22 [1], tuy nhiên các xác suất trong các kiểm tra này chỉ đúng cho các mẫu đặc biệt và cần được tính lại cho các mẫu khác. Trong [2], các tác giả đã đề xuất các tiêu chuẩn thống kê so khớp mẫu mới cho tất cả các mẫu 4 bit. Các kiểm tra mới này áp dụng cho chuỗi bất kỳ có độ dài tối thiểu là 5504 bit, trong khi theo NIST độ dài tối thiểu 106 bit. Trong bài báo này, chúng tôi đã cải tiến và đề xuất các kiểm tra so khớp mẫu 4 bit mới mà có thể áp dụng cho các chuỗi bất kỳ có độ dài nhỏ nhất chỉ là 3726 bit. Hơn nữa, chúng tôi đưa ra 3 kiểm tra thống kê so khớp mẫu 5 bit mới. Kết quả lý thuyết và thực hành cho thấy các đề xuất cải tiến của chúng tôi là rất hiệu quả trong việc đánh giá tính ngẫu nhiên cho các bộ tạo số giả ngẫu nhiên. Abstract—Randomness tests related to overlapping template matching have been proposed in NIST SP 800-22 [1], however the probabilities in these tests are only valid for specific samples and should be recalculated for other samples. In [2], the authors proposed new template matching tests for all 4-bit templates. The new tests can be applied to any sequence of minimum length of 5504 bits whereas the overlapping template matching test in the NIST test suite can only be applied to sequences of minimum length of 106 bits. In this paper, we have modified and proposed new 4-bit template matching tests that can be applied to any sequence of minimum length 3726 bits. Furthermore, we proposed three new 5-bit template matching tests. Our theoretical and practical results show that our new proposed tests are very efficient in psedorandom number generator testing.

Mối liên hệ giữa tính nhận biết tiền ảnh và một số tính chất mật mã khác của hàm băm

Tóm tắt—Các kiểm tra liên quan đến so khớp mẫu chồng lấp đã được đề xuất trong NIST SP 800-22 [1], tuy nhiên các xác suất trong các kiểm tra này chỉ đúng cho các mẫu đặc biệt và cần được tính lại cho các mẫu khác. Trong [2], các tác giả đã đề xuất các tiêu chuẩn thống kê so khớp mẫu mới cho tất cả các mẫu 4 bit. Các kiểm tra mới này áp dụng cho chuỗi bất kỳ có độ dài tối thiểu là 5504 bit, trong khi theo NIST độ dài tối thiểu 106 bit. Trong bài báo này, chúng tôi đã cải tiến và đề xuất các kiểm tra so khớp mẫu 4 bit mới mà có thể áp dụng cho các chuỗi bất kỳ có độ dài nhỏ nhất chỉ là 3726 bit. Hơn nữa, chúng tôi đưa ra 3 kiểm tra thống kê so khớp mẫu 5 bit mới. Kết quả lý thuyết và thực hành cho thấy các đề xuất cải tiến của chúng tôi là rất hiệu quả trong việc đánh giá tính ngẫu nhiên cho các bộ tạo số giả ngẫu nhiên. Abstract—Randomness tests related to overlapping template matching have been proposed in NIST SP 800-22 [1], however the probabilities in these tests are only valid for specific samples and should be recalculated for other samples. In [2], the authors proposed new template matching tests for all 4-bit templates. The new tests can be applied to any sequence of minimum length of 5504 bits whereas the overlapping template matching test in the NIST test suite can only be applied to sequences of minimum length of 106 bits. In this paper, we have modified and proposed new 4-bit template matching tests that can be applied to any sequence of minimum length 3726 bits. Furthermore, we proposed three new 5-bit template matching tests. Our theoretical and practical results show that our new proposed tests are very efficient in psedorandom number generator testing.

Design and Analysis of Earthing System for Wind Turbine Generators from Lightning Discharge Currents

<p>Currently, wind power production is undergoing rapid growth due to the escalating interest in green energy generation. As a result, generators are now choosing to locate wind turbine generators (WTGs) in areas where there is more lightning activity, and earthing problems can be exacerbated further by the soil resistivity being higher than where turbines are usually located. In addition, the desire to capture more energy from the wind has given way to larger WTGs, further increasing the probability of lightning strikes to the structure. This heightened regularity has emphasized the need for an effective grounding system, capable of dissipating the large currents discharged by the lightning into the lightning protection system. This “effective grounding system” must offer a low impedance by limiting the ground potential rise, which is critical due to the wider frequency content of the lightning discharge currents (ranging from DC to several MHz). The design of an effective grounding system for WTGs depends on the calculation of the minimum length of the earth electrodes, soil resistivity and its frequency-dependency, and the impact of WTG foundation. The calculation of the length of earth electrodes needs an accurate measurement of soil resistivity and modeling of the measured resistivity. Hence, this research considers the measured soil resistivity values of an Australian wind farm and presents an analysis of the soil stratification to identify the optimum soil models. The influence of the soil layers on the WTG grounding system is also investigated to install the earth electrodes. As the resistivity of the soil is frequency-dependent, an analysis is performed to evaluate the effect of the frequency-dependent soil parameters on the WTG grounding system at various frequencies of lightning discharge current. In addition, the impact of the rebar of the WTG foundation on the grounding system is evaluated as the rebar shares the lightning discharge currents. The effective length of the earth electrodes is frequency-dependent, and rebar determines the impedance of the grounding system at high-frequencies. The next step in the grounding design is the design of earth electrodes. The current dissipating capacity of the earth electrodes depends on soil resistivity, dimensions of the earth electrodes, and burial depth of the electrodes. However, the traditional practice of designing earth electrodes is based on the soil resistivity alone, considering the uniform soil resistivity model. The conventional method of designing earth electrodes based on the uniform soil resistivity is not practical due to non-homogeneous behavior of the soil resistivity. To enhance the WTG earthing system design, this research proposes a novel method to calculate the minimum length of an earth electrode for uniform and two-layer based soil models considering electrode dimensions and burial depth. The grounding impedance achieved when electrode lengths are calculated using the proposed method is compared to grounding impedance values computed using the conventional method. This comparison shows that the proposed method is an improvement on the current convention. In particular, the proposed method gives a grounding impedance value of less than 10 Ω at low frequencies for all soil resistivity values. This results in a reduction in the potential rise of up to 64% compared to the peak potential value in the conventional method. The benefits offered by the proposed method mean that it can be employed to calculate electrode lengths for the required resistance values based on soil resistivity, electrode dimensions, and burial depth. Such a design may serve as a starting point for an engineer wishing to design a WTG earthing system. Another challenge noted is the practice of assessing the effectiveness of the WTG grounding system. The conventional method is based on achieving a low-frequency resistance of 10 Ω according to the standard IEC 61400-24 and the performance of the grounding system at high frequencies is not considered. Hence, identification of the high-frequency components of the relevant lightning discharge currents is important to understand the performance of the grounding system. An analysis of the wind turbine earthing system for different lightning discharge current wave shapes is performed considering the lightning current waveforms and parameters mentioned in the IEC 61400-24 standard and evaluated the various frequency components and their influence on the WTG grounding system. It is identified that the impedance of the grounding system is minimum for the first short positive stroke current parameters for all the soil resistivity values compared to the first short negative and the subsequent short current wave shapes, although the peak current magnitude is highest for this wave shape. From the analysis of WTG grounding system based on various parameters, this research presents a procedure for assessing the effectiveness of WTG lightning protection system with a focus on the grounding system. It is identified that the effectiveness of the grounding system can be improved by proper design of earth electrodes, optimum soil stratification, and selecting low resistivity soil sites. Finally, various earth electrode configurations are evaluated to identify the better electrode configuration for WTG grounding system. This thesis provides an in-depth analysis of WTG grounding systems to protect WTGs from lightning strikes. The contributions of this research will help wind farm architects to design effective grounding systems leading to effective lightning protection systems. Finally, the contributions will help to increase the adoption of wind power, resulting in more renewable energy generation. The outcome of this research can be realized to reduce the downtime of WTGs by incorporating the effectiveness of lightning protection system component into the wind farm optimization process. Also, a generalized procedure for calculating the minimum length of earth electrodes for all the soil models can be developed in the future.</p>

Design and Analysis of Earthing System for Wind Turbine Generators from Lightning Discharge Currents

<p>Currently, wind power production is undergoing rapid growth due to the escalating interest in green energy generation. As a result, generators are now choosing to locate wind turbine generators (WTGs) in areas where there is more lightning activity, and earthing problems can be exacerbated further by the soil resistivity being higher than where turbines are usually located. In addition, the desire to capture more energy from the wind has given way to larger WTGs, further increasing the probability of lightning strikes to the structure. This heightened regularity has emphasized the need for an effective grounding system, capable of dissipating the large currents discharged by the lightning into the lightning protection system. This “effective grounding system” must offer a low impedance by limiting the ground potential rise, which is critical due to the wider frequency content of the lightning discharge currents (ranging from DC to several MHz). The design of an effective grounding system for WTGs depends on the calculation of the minimum length of the earth electrodes, soil resistivity and its frequency-dependency, and the impact of WTG foundation. The calculation of the length of earth electrodes needs an accurate measurement of soil resistivity and modeling of the measured resistivity. Hence, this research considers the measured soil resistivity values of an Australian wind farm and presents an analysis of the soil stratification to identify the optimum soil models. The influence of the soil layers on the WTG grounding system is also investigated to install the earth electrodes. As the resistivity of the soil is frequency-dependent, an analysis is performed to evaluate the effect of the frequency-dependent soil parameters on the WTG grounding system at various frequencies of lightning discharge current. In addition, the impact of the rebar of the WTG foundation on the grounding system is evaluated as the rebar shares the lightning discharge currents. The effective length of the earth electrodes is frequency-dependent, and rebar determines the impedance of the grounding system at high-frequencies. The next step in the grounding design is the design of earth electrodes. The current dissipating capacity of the earth electrodes depends on soil resistivity, dimensions of the earth electrodes, and burial depth of the electrodes. However, the traditional practice of designing earth electrodes is based on the soil resistivity alone, considering the uniform soil resistivity model. The conventional method of designing earth electrodes based on the uniform soil resistivity is not practical due to non-homogeneous behavior of the soil resistivity. To enhance the WTG earthing system design, this research proposes a novel method to calculate the minimum length of an earth electrode for uniform and two-layer based soil models considering electrode dimensions and burial depth. The grounding impedance achieved when electrode lengths are calculated using the proposed method is compared to grounding impedance values computed using the conventional method. This comparison shows that the proposed method is an improvement on the current convention. In particular, the proposed method gives a grounding impedance value of less than 10 Ω at low frequencies for all soil resistivity values. This results in a reduction in the potential rise of up to 64% compared to the peak potential value in the conventional method. The benefits offered by the proposed method mean that it can be employed to calculate electrode lengths for the required resistance values based on soil resistivity, electrode dimensions, and burial depth. Such a design may serve as a starting point for an engineer wishing to design a WTG earthing system. Another challenge noted is the practice of assessing the effectiveness of the WTG grounding system. The conventional method is based on achieving a low-frequency resistance of 10 Ω according to the standard IEC 61400-24 and the performance of the grounding system at high frequencies is not considered. Hence, identification of the high-frequency components of the relevant lightning discharge currents is important to understand the performance of the grounding system. An analysis of the wind turbine earthing system for different lightning discharge current wave shapes is performed considering the lightning current waveforms and parameters mentioned in the IEC 61400-24 standard and evaluated the various frequency components and their influence on the WTG grounding system. It is identified that the impedance of the grounding system is minimum for the first short positive stroke current parameters for all the soil resistivity values compared to the first short negative and the subsequent short current wave shapes, although the peak current magnitude is highest for this wave shape. From the analysis of WTG grounding system based on various parameters, this research presents a procedure for assessing the effectiveness of WTG lightning protection system with a focus on the grounding system. It is identified that the effectiveness of the grounding system can be improved by proper design of earth electrodes, optimum soil stratification, and selecting low resistivity soil sites. Finally, various earth electrode configurations are evaluated to identify the better electrode configuration for WTG grounding system. This thesis provides an in-depth analysis of WTG grounding systems to protect WTGs from lightning strikes. The contributions of this research will help wind farm architects to design effective grounding systems leading to effective lightning protection systems. Finally, the contributions will help to increase the adoption of wind power, resulting in more renewable energy generation. The outcome of this research can be realized to reduce the downtime of WTGs by incorporating the effectiveness of lightning protection system component into the wind farm optimization process. Also, a generalized procedure for calculating the minimum length of earth electrodes for all the soil models can be developed in the future.</p>

Expectation values of minimum-length Ricci scalar

In this paper, we consider a specific model, implementing the existence of a fundamental limit distance [Formula: see text] between (space or time separated) points in spacetime, which in the recent past has exhibited the intriguing feature of having a minimum-length Ricci scalar [Formula: see text] that does not approach the ordinary Ricci scalar [Formula: see text] in the limit of vanishing [Formula: see text]. [Formula: see text] at a point has been found to depend on the direction along which the existence of minimum distance is implemented. Here, we point out that the convergence [Formula: see text] in the [Formula: see text] limit is anyway recovered in a relaxed or generalized sense, which is when we average over directions, this suggesting we might be taking the expectation value of [Formula: see text] promoted to be a quantum variable. It remains as intriguing as before the fact that we cannot identify (meaning this is much more than simply equating in the generalized sense above) [Formula: see text] with [Formula: see text] in the [Formula: see text] limit, namely, when we get ordinary spacetime. Thing is like if, even when [Formula: see text] (read here the Planck length) is far too small to have any direct detection of it feasible, the intrinsic quantum nature of spacetime might anyway be experimentally at reach, witnessed by the mentioned special feature of Ricci, not fading away with [Formula: see text] (i.e. persisting when taking the [Formula: see text] limit).