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In the field of Complex Analysis, it is acknowledged that Cauchy’s Residue Theorem plays an essential role, which allows the calculation of complex integrals by adding up the residues of singularities in the complex plane. Many mathematicians have developed various theorems out of Cauchy’s Residue Theorem and have solved numerous problems using Cauchy’s Residue Theorem, but there are still a lot more studies needed. Thus, this paper focuses on examining Residue Theorem deeply by introducing singularity point and residue, combining Laurent series and complex integral, then deducting Cauchy’s Residue Theorem. This paper then concentrates on solving four unique complex integrals to illustrate Cauchy’s Residue Theorem by analyzing the graph of integration, reformatting the integrals, applying theorems or tricks, integrating the reformatted integrals, and simplifying the results. As a result, this paper not only presented a deeper analysis of the deduction of Cauchy’s Residue Theorem, but also presented the solutions towards four previously unsolved complex integrals. The deduction of Cauchy’s Residue Theorem and the four complex analysis problems have important applications for dealing with integrals associated with hyperbolic functions and lead to future research in other areas of mathematics and physics.

Low-e products have been accepted widely as an energy-efficient solution or energy retrofitting strategy for glazing systems, including single-pane windows, which may reduce the emission of radiant infrared energy and improve the insulating properties of overall windows. However, the addition of a low-e layer may increase the condensation risk, and in turn, significantly diminish the window’s thermal performance. To better understand the condensation effects of low-e windows on overall building energy use, we extended the classic Nusselt filmwise condensation model to establish and validate a simplified double-film-based analytical model, and then characterized the condensation-dependent thermal dynamics of low-e coated single-pane glazing. A series of whole building energy use comparisons between simulations ignoring and considering the condensation effect were conducted. The results indicate that if the condensation effect is taken into account, the low-e single-pane glazing may lead to adverse effects on the energy-saving purpose in certain climates relative to the original single-pane glazing. More careful and comprehensive energy analyses are needed to use low-e products for window energy retrofits.

With the recent discoveries and engineering solutions emerging in nanomaterials and nanostructures, independent band modulation of solar radiation on building envelopes, including glazing systems, has become increasingly viable as a potential means of improving building energy savings and indoor visual comfort. However, when it comes to the prediction of these new materials’ potential energy performance in buildings, most studies utilize a simple solar irradiance (e.g., global horizontal solar irradiance, direct beam solar irradiance) or a rough estimation of solar infrared (e.g., 50% solar irradiance) as input, which may cause significant errors. Consequently, there is a pressing need for reliable performance estimations of the solar infrared control and response at the building’s scale. To assess this, we need a solar spectral irradiance model, or at least a wideband (visible or infrared) solar irradiance model, as input. To develop this new type of model, one needs to understand the modeling-related key elements, including available solar spectral irradiance datasets, data collection methods, and modeling techniques. As such, this paper reviews the current major measurement methods and tools used in collecting solar spectral irradiance data with a focus on the solar infrared region, identifies the available related resources and datasets that particularly encompass the solar spectral irradiance data with a sufficient wavelength range, and studies existing solar irradiation modeling techniques for building simulations. These investigations will then form the background and backbone for a study scheme of solar infrared radiation modeling and indicate future research paths and opportunities.

The curvilinear roofs of ancient Chinese wooden architecture feature unique functional, hierarchical, and aesthetic elements. However, the digitalization of these roofs has yet to be explored because of the lack of accurate mathematical models for these roof geometries. This research aims to parameterize the design and construction rules for these roofs as stipulated in the Yingzao fashi. We first illustrate the major features of curvilinear roofs, followed by a comprehensive investigation on the raising and bending rules via the original texts and drawing samples provided in the Yingzao fashi and the Annotated yingzao fashi by Sicheng Liang. Then, the mathematical models are developed. The main contribution of this research is the transformation of the design and building rules for complex curvilinear roofs into mathematical models, enabling designers to generate such roof architecture and adding new insights to existing mathematical methods in studying ancient architecture.

In order to further understand the effects of drought stress on hydraulic characteristics and the relationship between hydraulic conductivity and aquaporins or water channels of root systems of three wolfberry cultivars (Lycium chinense Mill.), hydraulic conductivity of 2-year-old pot-grown seedlings was measured under drought stress, rewatering, and treatment with exogenous mercuric chloride and β-mercaptoethanol. Under moderate and severe drought stress levels, the most significant decrease of hydraulic conductivity was 37.3% and 24.0%, respectively, in the ‘Ningqi 5’ cultivar compared with the non-stressed control. After rewatering, the rate of recovery in specific conductivity was most rapid in the ‘Mengqi 1’ cultivar, at 0.058 and 0.072 kg MPa−1 m−2 s−1 h−1 under moderate and severe drought stress levels, respectively. The ‘Mengqi 1’ cultivar had the highest recovery degree of hydraulic conductivity under two concentrations of β-ME (500 or 1000 μmol L− 1), reaching 82.4% and 88.5%, respectively, of the initial conductivity. The adaptive capacity of hydraulic conductivity in the ‘Ningqi 5’ cultivar was weaker than in the ‘Ningqi 1’ and ‘Mengqi 1’ cultivars under drought stress. The recovery capacity of hydraulic conductivity in ‘Mengqi 1’ cultivar was stronger than the ‘Ningqi 1’ and ‘Ningqi 5’ cultivars after rewatering. Aquaporins of the ‘Ningqi 1’ cultivar root systems had the highest binding affinity with mercuric chloride, which was the most likely cause in the decrease in hydraulic conductivity, whereas aquaporins of ‘Mengqi 1’ root systems had the weakest binding affinity. The inhibitory effect of mercuric chloride was readily eliminated by β-mercaptoethanol in the ‘Mengqi 1’ cultivar. The hydraulic characteristics of this cultivar were more sensitive to drought, mercuric chloride and β-mercaptoethanol than the other cultivars.

In arid areas of China, water shortage and heavy carbon emissions have been threatening agricultural sustainability and which has become a vital issue. A field experiment was conducted to explore how different mulching affects soil moisture and temperature, CO2 fluxes, forage-maize hay yield and nutritional value during 2 consecutive years: 2014 and 2015. The field experiment showed that mulching materials had distinct effects on soil moisture and temperature and CO2 fluxes. The soil temperature and CO2 fluxes were in order of common plastic film mulching (PFM) > bio-degradable mulch mulching (BMM) > no mulching (CK) > straw mulching (SM), while the soil moisture was in order of PFM > BMM > SM > CK over these two years. Compared with CK, hay yield respectively increased by 23.25%, 22.51% and 5.27% for PFM, BMM and SM, WUE increased by 35.60%, 32.34% and 10.88%, and the total nutrient yields increased by 17.75%, 21.35% and 6.95%, respectively. To sum up, in combination with ecology and environmental protection, bio-degradable mulch could replace common plastic film and bio-degradable mulch should be popular in future. As bio-degradable mulch is green non-pollution, it is conducive to the sustainable development of agricultural ecosystem.

Windows not only mediate thermal transfer, light transmission, noise control, and natural ventilation but also serve as an architectural element affecting a structure’s aesthetics and appearance. Since the glazed window was first developed in Egypt in 100 AD, the thermal and optical performance of windows have been primary concerns for architects, engineers, and researchers. Today, windows are of special note because of their relationship to building sustainability and energy-efficient design. According to recent National Fenestration Rating Council reports, due to the relatively lower thermal insulation among all building envelope components, windows are normally responsible for 25–30% of the total heating, ventilation, and air conditioning energy use. This non-neglectable use of energy has motivated researchers to investigate various energy-efficient technologies and design solutions. Windows gain and lose heat through conduction, convection, and radiation. These properties can be measured and rated according to the following energy performance characteristics: insulating value, heat gain from solar radiation, and air infiltration rate. Conversely, the optical properties of windows determine their interaction with light and indoor occupants. The visible transmittance (corresponding to the fraction of impinging visible solar radiation transmitted) and haze value (meaning the clarity of the window) must both be taken into account. Most technology modulating the optical properties of windows also affects their thermal properties. Thus, the process of designing and engineering building windows is uniquely complex, involving both thermal and optical behaviors that affect building energy use, occupant comfort, and architectural aesthetics.

Solar near-infrared (NIR) selective glazing systems have been proposed by incorporating photothermal effects (PTE) of a nanoparticle film into building windows. From an energy efficiency perspective, the nanoscale PTE forms unique inward-flowing heat by heating up the window interior surface temperature under solar near-infrared, significantly improving the window thermal performance. Also, the PTE-driven solar heat gains are dynamic upon solar radiation and weather conditions. However, the PTE on annual building energy use has not been investigated thoroughly, due to the lack of an accurate and appropriate energy simulation method. In this study, we used the EnergyPlus energy management system to develop a parametric energy model and simulation approach in which a solar-temperature-dependent thermal model was embedded into the parametric energy simulation workflow. Applying this method, we examined the solar near-infrared-dependent PTE-induced thermal performances of glazing systems and their effects on annual heating energy use in representative cold climates (i.e., Zones 4, 5, and 6). The results show that the dynamic model considering the PTE demonstrated more heating energy savings, up to 11.64% in cold climates, as opposed to the baseline model that ignored the PTE. This work presents a method to model and simulate the dynamic thermal performance of windows with PTE.

Thin films made of metallic nanoparticles can exhibit strong photothermal effects (PPE) on near-infrared light irradiation, paving a way for new designs of spectrally selective building windows for solar infrared modulation that operates without the need to compensate for visible transmittance. More importantly, the surface plasmon-induced light-to-heat conversion creates strong localized heating effects with a much smaller fraction resulting in the heating of the substrate. Incorporating such nanoscale PPE into the design of complex building fenestrations, this research conducted a comprehensive analysis to better understand the PPE-induced heating effect and conductive, convective, and radiative heat exchanges between windowpane surfaces and the surrounding indoor and outdoor environments. The authors first developed and then validated a numerical analysis method to incorporate spectral features, solar spectral irradiance, and nanoscale PPE. Subsequently, using the established numerical method, two-dimensional windowpane temperature profiles and solar heat gains were yielded under different boundary conditions. To understand the energy performance of windows with solar near-infrared-dependent PPE, a series of parametric energy simulations was employed. The results show the photothermal coating can be used as a new energy-efficient retrofit technology for single-pane windows, with heating energy saving 16.2–20.8%, which performs similar to the double pane windows. Notably, these energy savings were not achieved by increasing the thermal insulation via additional layers or insulating materials, but rather by the spectrally selective design of glazing materials and utilization of solar near-infrared energy. This work presents the energy saving mechanism on an architectural scale due to the nanoscale surface plasmon-induced photothermal effect and associated heat gain coefficient enhancement. It also poses a fundamental reference for the future integration of this novel nanoscale phenomenon into the building envelope systems.

Shape memory polymers (SMPs) have attracted significant attention from both industrial and academic researchers, due to their useful and fascinating functionality. One of the most common and studied external stimuli for SMPs is temperature; other stimuli include electric fields, light, magnetic fields, water, and irradiation. Solutions for SMPs have also been extensively studied in the past decade. In this research, we review, consolidate, and report the major efforts and findings documented in the SMP literature, according to different external stimuli. The corresponding mechanisms, constitutive models, and properties (i.e., mechanical, electrical, optical, shape, etc.) of the SMPs in response to different stimulus methods are then reviewed. Next, this research presents and categorizes up-to-date studies on the application of SMPs in dynamic building structures and components. Following this, we discuss the need for studying SMPs in terms of kinetic building applications, especially about building energy saving purposes, and review recent two-way SMPs and their potential for use in such applications. This review covers a number of current advances in SMPs, with a view towards applications in kinetic building engineering.

a b s t r a c t Alfalfa (Medicago sativa L.) is traditionally sown in field without ridge and furrow, in rain-fed semi-arid areas of Northwest China, and forage yields are normally low because of drought, water loss and soil erosion. A field study was conducted to determine (1) Monthly runoff efficiency and threshold rainfall for different ridge widths (30, 45 and 60 cm), and mulched with different materials (common plastic film, bio-degradable mulching film and manually compacted soil); and (2) the effects of different ridge-furrow ratios (30:60, 45:60 and 60:60) and ridge-mulching materials on soil water storage, topsoil temperature, forage yields, and water use efficiency (WUE) of Alfalfa in ridge-furrow rainwater harvesting (RFRWH) system, during 2 consecutive years: 2012 and 2013. Average monthly runoff efficiency over these 2 years, was 16%, 18%, 19%, 65%, 71%, 77%, 70%, 72% and 79% for SR30, SR45, SR60, BMR30, BMR45, BMR60, CMR30, CMR45 and CMR60 (SR, BMR and CMR were ridges with manually compacted soil, mulched with bio- degradable mulch film and common plastic film, respectively, and subscripts 30, 45 and 60 refer to ridge widths (cm) all with 60 cm furrow width), respectively. For the same treatments, threshold rainfall was 4.3, 4.3, 4.2, 3.0, 2.9, 2.8, 2.9, 2.9 and 2.8 mm. The field experiment showed that ridge mulching materials and ridge widths had distinct effects on topsoil temperature at ridge tops, but not at furrow bottoms. Soil water storage in 140 cm soil depth at furrow bottoms increased with increasing ridge width and in the order of CMR ≈ BMR > SR > FP. Average annual total forage yields for FP, SR, BMR and CMR were 6276, 5642, 7563 and 7817 kg ha−1, respectively, over 2 years. The total precipitation in both years was higher than average of rainfall, leading to significant decreases of forage yields for SR, and significant increases of forage yields for BMR and CMR. Compared with FP, average forage yields decreased by 3%, 10% and 17% for SR30, SR45 and SR60, and increased by 27%, 21%, 13%, 32%, 26% and 16% for BMR30, BMR45, BMR60, CMR30, CMR45 and CMR60, respectively, over 2 years. WUE for SR, BMR and CMR was 1.69, 1.74 and 1.74 times greater than that for FP over 2 years, and increased with decreasing ridge width. Optimum furrow width was 35-36 cm for CMR and BMR in the RFRWH system with 60 cm width furrows for Alfalfa production in this region. Future study is needed to investigate optimum ridge-furrow ratio and suitable ridge- mulching material for achieving the best environmental and economic benefit under different climatic conditions, soil types and plant species, and using bio-degradable mulching materials.

Monitoring of drinking water has shown an increase in nitrate-nitrogen (NO 3 − -N) concentration in groundwater in some areas of the Heihe River Basin, Northwest China. A combination of careful irrigation and nitrogen (N) management is needed to improve N uptake efficiency and to minimize fertilizer N loss. A 2-year experiment investigated the effects of different irrigation and N application rates on soil NO 3 − -N distribution and fertilizer N loss, wheat grain yield and N uptake on recently reclaimed sandy farmland. The experiment followed a completely randomized split-plot design, taking flood irrigation (0.6, 0.8 and 1.0 of the estimated evapotranspiration) as main plot treatment and N-supply as split-plot treatment (with five levels of 0, 79, 140, 221, 300 kg N ha−1). Fertilizer N loss was calculated according to N balance equation. Our results showed that, under deficit irrigation conditions, N fertilizer application at a rate of 300 kg ha−1 promoted NO 3 − -N concentration in 0–200 cm depth soil profiles, and treatments with 221 kg N ha−1 also increased soil NO 3 − -N concentrations only in the surface layers. Fertilizer N rates of 70 and 140 kg ha−1 did not increase NO 3 − -N concentration in the 0–200 cm soil profile remaining after the spring wheat growing season. The amount of residual NO 3 − -N in soil profiles decreased with the amount of irrigation. Compared with N0, the increases of fertilizer N loss, in N79, N140, N221 and N300 respectively, were 59.9, 104.6, 143.5 and 210.6 kg ha−1 over 2 years. Under these experimental conditions, a N rate of 221 kg ha−1 obtained the highest values of grain yield (2775 kg ha−1), above-ground dry matter (5310 kg ha−1) and plant N uptake (103.8 kg ha−1) over 2 years. The results clearly showed that the relative high grain yield and irrigation water productivity, and relative low N loss were achieved with application of 221 kg N ha−1 and low irrigation, the recommendation should be for those farmers who use the upper range of the recommended 150–400 kg N ha−1, that they can save about 45% of their N and 40% of their irrigation water application.

A field study was conducted to determine runoff efficiency and the effects of different ridge: furrow ratios and ridge-covering materials on tuber yield, soil moisture storage and water use efficiency (WUE) in the ridge and furrow micro-water harvesting system in a dry semi-arid region of China, during two consecutive years of 2002 and 2003. The average runoff efficiency of ridges with compacted soil (SR) was very low (24.6–28.8%) compared to that of ridges covered with plastic film (MR) (91.1–94.3%). The minimal rainfall necessary to produce runoff was 2.76–2.78 mm for SR, only 0.23–0.47 mm for MR. The field experiments using potato as an indicator crop showed that tuber yields in the MR system were significantly higher than that in the flat planting (control), with an average increase of 158.6–175.0% during 2 years. In the SR system, the average increase was valued of 14.9–28.4% during 2 years. Regression analysis between tuber yields and ridge widths indicated the optimum ridge: furrow ratio for MR was 39: 60 cm in 2002 and 48: 60 cm in 2003 respectively. The WUE values of potato in MR were 1.50 times greater than that of the controls in 2002 and 1.62 times greater than the controls in 2003. No differences were found in the WUE between the SR and the controls on average of 2 years. Due to the different runoff efficiency between two ridge-covering materials and absence of runoff occurrence in the controls, the soil water content in the MR was higher than that in the SR, both of which were greater than the controls. With the soil crust development, the distribution of soil water at the bottom of the furrow, at the side of the furrow and at the top of the ridge, is similar between the SR and the MR.

In this work, a simple two-step route has been developed to synthesize ultrafine barium titanate (BaTiO 3 ) with size ranging from 30 nm to 100nm by reacting barium hydroxide with tetrabutyl titanate in mixing solvent. This method facilitates the process-control and the property tailoring of the particles. The effect of 1,4-butylene glycol on hydrolysis rate of tetrabutyl titanate, temperature, solvent ratio between isopropanol and water, the particle size, the crystalline phase have been investigated. The prepared BaTiO 3 nanoparticles were characterized using X-ray diffraction and scanning electron microscopy (SEM). The results show that the particle size can be easily tuned by adjusting the ratio of 1, 4-butylene glycol, isopropanol and water in solution. The dielectric behavior of the BaTiO 3 /PVDF at low frequency show that the interfacial polarization acts as an important role for the high dielectric constant (e r ).

Intercropping of bread wheat (Triticum aestivum L.), maize (Zea mays L.) and potato (Solanum tuberosum)has been practiced in North-West China in the last several decades; however, the effects of this intercropping and phosphorus addition on crop yield and some wheat-grain components have not been adequately investigated. A 2-year field experiment was conducted from 2002 to 2003 in irrigated areas in North-West of China to investigate how phosphorus fertilizer application and intercropping of wheat/maize/potato impact on the crop yield and wheat-grain components such as protein content, wet gluten and sodium dodecyl sulphate (SDS) sedimentation. The results indicated that bread wheat and maize achieved higher yields in the intercropping system than in the monoculture system over the 2 years, and the wheat-grain had higher protein content, wet gluten and sodium dodecyl sulphate (SDS) sedimentation in the intercropping system than in the monoculture system. Better utilization of resources through border row effect and preventing competition between species over growing period have been indicated as the major factors contributing to the increased crop yield and wheat-grain components. Phosphorus application significantly increased crop yields and improved wheat-grain components; however, the optimal application rate for achieving highest protein content was at 150 kg ha-1. The practical implication of the present study was that to obtain good yield and better wheat-grain components, a combination of intercropping and application of phosphorus fertilizer at a rate of approximately 150 kg ha-1 was found as one of the most practical options. Key words: Border-row effect, intercropping, phosphorus, wheat-grain components, wheat/maize/potato, yield.

The ecological mechanism of competition and compensation between the crop root systems of two different intercropping patterns, wheat-soybean and corn-cabbage, was studied by field experiment. The results showed that the annual growth peak of wheat-soybean roots in intercropping was interlacing, the growth of root weight and length expressed synchronism, and the peak of root weight was appeared earlier than that of root length. The vertical distribution of the two crops' root system in two intercroppings was reduced gradually along with soil depths, which also showed that the multiple growth waves moved progressively. The root system distributed horizontally in intercropping system also showed a clearly unbalanced distribution. The root system distribution of out-row for corn elongated 20.4-40.8 cm to cabbage rows, but that of cabbage elongated only 8.5-12.6 cm to corn. The cross extent of root systems in corn-cabbage intercropping was decreased from 40.2 cm to 20.1 cm by fertilization, and the place of cross point for root concentrated region was changed from 20.5 cm to 12.4 cm below soil surface by fertilizer supply. The place of cross point for root concentrated region was an important index to decide the degrees of competition.