Nonlinear Sum Research Articles

Existence of the non‐radially symmetric ground state for p‐Laplacian equations involving Choquard type

We consider some p‐Laplacian type equations with sum of nonlocal term and subcritical nonlinearities. We prove the existence of the ground states, which are positive. Because of including p=2, these results extend the results of Li, Ma and Zhang [Nonlinear Analysis: Real World Application 45(2019) 1‐25]. When p=2, N=3, by a variant variational identity and a constraint set, we can prove the existence of a non‐radially symmetric solution. Moreover, this solution u(x1, x2, x3) is radially symmetric with respect to (x1, x2) and odd with respect to x3.

The article

Normally the sum of ratios problems are reduced into a sequence of single-ratio problems and then solved by existing methods. Because of their combinatorial nature, the computational complexity grows exponentially. A sum of non-linear fractional function optimization problem with several fractions is proved to be a NP-complete problem indicating that an efficient algorithm may not exist. The non-linear sum of fractional functions are linearized by piecewise linearization technique and converted into a linear sum of fractional programming problem. Optimal solution is found at for the new problem. The number of iterations depends on the contribution of decision variables to objective function value

The Prevailing Role of Hotspots in Plasmon-Enhanced Sum-Frequency Generation Spectroscopy.

The plasmonic amplification of nonlinear vibrational sum frequency spectroscopy (SFG) at the surfaces of gold nanoparticles is systematically investigated by tuning the incident visible wavelength. The SFG spectra of dodecanethiol-coated gold nanoparticles chemically deposited on silicon are recorded for 20 visible wavelengths. The vibrational intensities of thiol methyl stretches extracted from the experimental measurements vary with the visible color of the SFG process and show amplification by coupling to plasmon excitation. Because the enhancement is maximal in the orange-red region rather than in the green, as expected from the dipolar model for surface plasmon resonances, it is attributed mostly to hotspots created in particle multimers, in spite of their low surface densities. A simple model accounting for the longitudinal surface plasmons of multimers allows the recovery of the experimental spectral dispersion.

An in situ IR-Vis Sum Frequency Generation Spectroscopy study of cyanide adsorption during zinc electrodeposition

In this paper, we demonstrate the feasibility of in situ non-linear IR-Vis Sum Frequency Generation (SFG) Spectroscopy investigations at zinc surfaces in electrochemical ambient. We investigated both zinc electrodeposition onto an extraneous electrode and adsorption on polycrystalline zinc. Electrodeposition studies were carried out onto a polycrystalline gold cathode in contact with a Zn-cyanocomplex solution containing free CN−, while adsorption studies were carried out on a polycrystalline zinc electrode in contact with a free-CN− solution. In both experiments, we monitored the spectroscopic features associated with the internal stretching of the adsorbed cyanide (ca. 2100 cm−1) that we exploited as local Au and Zn site probes. Spectroelectrochemical results were complemented by cyclic voltammetric measurements. This proof-of-principle study is encouraging in the view of more concrete applications regarding additive adsorption at zinc electrodes, aiming at a fundamental understanding of the cycling stability of zinc battery anodes.

A time domain study of surfactin penetrating a phospholipid monolayer at the air-water interface investigated using sum frequency generation spectroscopy, infrared reflection absorption spectroscopy, and AFM-nano infrared microscopy

We have investigated the interaction of surfactin with a monolayer of 1,2-dipalmitoyl-sn-glycero-3-phosphocholine (DPPC) at the air-water interface as a function of time, following its injection into the sub-phase, using non-linear Sum Frequency Generation (SFG) vibrational spectroscopy and Infrared Reflection Absorption Spectroscopy (IRRAS). SFG resonances from the phospholipid and from the surfactin were distinguished from each other by using selective deuteration. The surface pressure at the interface was measured concurrently for up to 8 h. After an induction period, the spectra from the lipid diminished and those of surfactin gradually appeared whilst at the same time the surface pressure increased. However, eventually the surfactin signals disappeared and those of the lipid reappeared. Although the SFG spectra of the lipid disappeared at intermediate times, the IRRAS spectra of the lipid were always present at the interface. Variation in the temporal SFG behaviour was investigated as the pH of the sub-phase, the initial surface pressure of the lipid, and the surfactin concentration were changed. Samples of the surface film were transferred onto mica substrates at selected times along the temporal profile and imaged by Atomic Force Microscopy - nano Infrared Spectroscopy (nano-IR). A model is proposed to account for the results from the four different experimental techniques used.

Molecular Mechanisms of Interactions between Monolayered Transition Metal Dichalcogenides and Biological Molecules.

Single layered two-dimensional (2D) materials such as transition metal dichalcogenides (TMDs) show great potential in many microelectronic or nanoelectronic applications. For example, because of extremely high sensitivity, TMD-based biosensors have become promising candidates for next-generation label-free detection. However, very few studies have been conducted on understanding the fundamental interactions between TMDs and other molecules including biological molecules, making the rational design of TMD-based sensors (including biosensors) difficult. This study focuses on the investigations of the fundamental interactions between proteins and two widely researched single-layered TMDs, MoS2, and WS2 using a combined study with linear vibrational spectroscopy attenuated total reflectance FTIR and nonlinear vibrational spectroscopy sum frequency generation vibrational spectroscopy, supplemented by molecular dynamics simulations. It was concluded that a large surface hydrophobic region in a relatively flat location on the protein surface is required for the protein to adsorb onto a monolayered MoS2 or WS2 surface with preferred orientation. No disulfide bond formation between cysteine groups on the protein and MoS2 or WS2 was found. The conclusions are general and can be used as guiding principles to engineer proteins to attach to TMDs. The approach adopted here is also applicable to study interactions between other 2D materials and biomolecules.

Nonlinear sum operator equations and applications to elastic beam equation and fractional differential equation

In this paper, by studying the solutions of the abstract operator equation A(x,x)+B(x,x)+e=x on ordered Banach spaces, where A, B are two mixed monotone operators and ein P with theta leq eleq h, we prove a class of boundary value problems on elastic beam equation to have a unique solution. Furthermore, we also apply our abstract result to establish the existence and uniqueness theorem of nontrivial solutions for nonlinear fractional boundary value problems. The iterative sequences to approximate unique solutions for the above two classes of problems are also obtained.

Evaluating the Predictive Accuracy of Corn Phenological Durations in Iowa and Illinois

Core IdeasThis paper evaluates the predictive accuracy of thermal heat sum indices. The data used is extensive both spatially (district level data for Iowa and Illinois) and temporally (period 1996–2016). This data is used to evaluate the predictive accuracy of several types of thermal heat sum indices (e.g., bilinear and non‐linear) for granular growth intervals. The evaluation is executed by a novel technique using out‐of‐sample contemporaneous forecasts. ABSTRACTThermal heat sum indices are used to predict the duration of corn (Zea mays L.) growth intervals. Surprisingly, there exists very few studies in agronomic literature that assess predictive accuracy of these indices. This paper contributes to this topic in several ways using USDA‐NASS corn growth data for Iowa (IA) and Illinois (IL) which together cover about 30% of corn production in the United States. First, the dataset spans from 1996 to 2016 and covers all the districts in both Iowa and Illinois. Second, the data are used to evaluate the predictive accuracy of several types of thermal heat sum indices (bilinear and nonlinear) for granular growth intervals. Third, the evaluation is executed using out‐of‐sample contemporaneous forecasts. The results show that nonlinear thermal heat sum indices (HSIs) have superior predictive accuracy to bilinear indices, whereas linear HSIs turn out to be inferior. Overall, the predicted durations using nonlinear thermal HSIs for the Iowa and Illinois combined districts are reasonably accurate. There is little bias across most of the growth intervals despite including the 2009 and 2012 growing seasons with extreme weather conditions. The mean absolute percentage error (MAPE) of the predicted durations relative to actual is well within 10% for almost all growth intervals across combined districts in IA and IL with a low MAPE of 5% for the full growing season duration using the nonlinear thermal heat sum indices. In comparison with other growth intervals, the vegetative growth interval has the lowest MAPE for both IA and IL combined districts.

Exponential sums related to Maass forms

We estimate short exponential sums weighted by the Fourier coefficients of a Maass form. This requires working out a certain transformation formula for non-linear exponential sums, which is of independent interest. We also discuss how the results depend on the growth of the Fourier coefficients in question. As a byproduct of these considerations, we can slightly extend the range of validity of a short exponential sum estimate for holomorphic cusp forms. The short estimates allow us to reduce smoothing errors. In particular, we prove an analogue of an approximate functional equation previously proven for holomorphic cusp form coefficients. As an application of these, we remove the logarithm from the classical upper bound for long linear sums weighted by Fourier coefficients of Maass forms, the resulting estimate being the best possible. This also involves improving the upper bounds for long linear sums with rational additive twists, the gains again allowed by the estimates for the short sums. Finally, we shall use the approximate functional equation to bound somewhat longer short exponential sums.

Disponibilidad de residuos forestales y su potencial para la generación de energía en los bosques templados de El Salto, Durango

Los residuos de la cosecha forestal son una fuente de energía renovable que no ha sido considerada todavía a gran escala en México y para su estimación se requiere de evaluaciones cada vez más precisas. En este estudio se desarrollaron ecuaciones para estimar el volumen de residuos forestales y se cuantificó la disponibilidad de biomasa y su potencial para generar energía eléctrica y reducir emisiones de CO2 en la región de El Salto, Durango. La metodología se dividió en tres fases: i) se obtuvo el volumen total autorizado de los programas de manejo forestal maderable de 20 ejidos de la región; ii) se derribaron y cubicaron 2156 árboles en las áreas de corta de los 20 ejidos para generar ecuaciones de volumen de residuos a escala de árbol individual; y iii) el volumen de residuos fue convertido a toneladas de biomasa empleando los valores de densidad de la madera para posteriormente transformar este valor a unidades de energía eléctrica. Dado que las especies estudiadas constituyen bosques mezclados, manejados con el mismo tratamiento silvícola y edad de rotación, se evaluaron las diferencias entre especies en las ecuaciones de volumen de residuos, utilizando el método de la suma adicional de cuadrados no lineales. Los parámetros de las ecuaciones de volumen de residuos fueron significativamente diferentes entre la mayoría de las especies. La cantidad de residuos a escala de árbol fue mayor en las especies del género Quercus, mientras que la cantidad de residuos forestales disponibles por ciclo de corta fue mayor en las especies del género Pinus. Alrededor de 31 000 Mg año-1 de residuos forestales pueden utilizarse en la región para generar aproximadamente 65.6 GW h año-1, considerando el uso de una tecnología con una eficiencia mínima de 40%.

Understanding Dissolution and Crystallization with Imaging: A Surface Point of View.

The tendency for crystallization during storage and administration is the most considerable hurdle for poorly water-soluble drugs formulated in the amorphous form. There is a need to better detect often subtle and complex surface crystallization phenomena and understand their influence on the critical quality attribute of dissolution. In this study, the interplay between surface crystallization of the amorphous form during storage and dissolution testing, and its influence on dissolution behavior, is analyzed for the first time with multimodal nonlinear optical imaging (coherent anti-Stokes Raman scattering (CARS) and sum frequency generation (SFG)). Complementary analyses are provided with scanning electron microscopy, X-ray diffraction and infrared and Raman spectroscopies. Amorphous indomethacin tablets were prepared and subjected to two different storage conditions (30 °C/23% RH and 30 °C/75% RH) for various durations and then dissolution testing using a channel flow-through device. Trace levels of surface crystallinity previously imaged with nonlinear optics after 1 or 2 days of storage did not significantly decrease dissolution and supersaturation compared to the freshly prepared amorphous tablets while more extensive crystallization after longer storage times did. Multimodal nonlinear optical imaging of the tablet surfaces after 15 min of dissolution revealed complex crystallization behavior that was affected by both storage condition and time, with up to four crystalline polymorphs simultaneously observed. In addition to the well-known α- and γ-forms, the less reported metastable ε- and η-forms were also observed, with the ε-form being widely observed in samples that had retained significant surface amorphousness during storage. This form was also prepared in the pure form and further characterized. Overall, this study demonstrates the potential value of nonlinear optical imaging, together with more established solid-state analysis methods, to understand complex surface crystallization behavior and its influence on drug dissolution during the development of amorphous drugs and dosage forms.

What the Diffuse Layer (DL) Reveals in Non-Linear SFG Spectroscopy

Following our recent work [Phys. Chem. Chem. Phys. 20:5190–99 (2018)] that provided the means to unambigously define and extract the three water regions at any charged interface (solid–liquid and air–liquid alike), denoted the BIL (Binding Interfacial Layer), DL (Diffuse Layer) and Bulk, and how to calculate their associated non-linear Sum Frequency Generation Spectroscopy (SFG) χ2(ω) spectroscopic contributions from Density Functional Theory (DFT)-based ab initio molecular dynamics simulations (DFT-MD/AIMD), we show here that the χDL2(ω) signal arising from the DL water region carries a wealth of essential information on the microscopic and macroscopic properties of interfaces. We show that the χDL2(ω) signal carries information on the surface potential and surface charge, the isoelectric point, EDL (Electric Double Layer) formation, and the relationship between a nominal electrolyte solution pH and surface hydroxylation state. This work is based on DFT-MD/AIMD simulations on a (0001) α–quartz–water interface and on the air–water interface, with various surface quartz hydroxylation states and various electrolyte concentrations. The conclusions drawn make use of the interplay between experiments and simulations. Most of the properties listed above can now be extracted from experimental χDL2(ω) alone with the protocols given in this work, or by making use of the interplay between experiments and simulations, as described in this work.

Multiobjective Nonlinear Sum of Fractional Optimization Problems with Nonconvex Constraints with the Use of the Duality-Based Branch and Bound Algorithm

We study the solution of a multiobjective nonlinear sum of fractional optimization problems. A dualitybased branch and bound cut method is developed for the efficient solution of this problems. The proposed methodology is validated by proving the required theoretical assertions for the solution. The present method is an extension of the work P. P. Shen, Y. P. Duan, and Y. G. Pei [J. Comput. Appl. Math., 223, 145–158 (2009)] developed for a single-objective sum of ratios of nonlinear optimization problems. The proposed method is realized in MatLab (version 2014b). Two numerical problems are considered and solved by using the proposed method and the global optimal solution is obtained.

Kinetic study of lipase-catalyzed glycerolysis of palm olein using Lipozyme TLIM in solvent-free system.

Diacylglycerol (DAG) and monoacylglycerol (MAG) are two natural occurring minor components found in most edible fats and oils. These compounds have gained increasing market demand owing to their unique physicochemical properties. Enzymatic glycerolysis in solvent-free system might be a promising approach in producing DAG and MAG-enriched oil. Understanding on glycerolysis mechanism is therefore of great importance for process simulation and optimization. In this study, a commercial immobilized lipase (Lipozyme TL IM) was used to catalyze the glycerolysis reaction. The kinetics of enzymatic glycerolysis reaction between triacylglycerol (TAG) and glycerol (G) were modeled using rate equation with unsteady-state assumption. Ternary complex, ping-pong bi-bi and complex ping-pong bi-bi models were proposed and compared in this study. The reaction rate constants were determined using non-linear regression and sum of square errors (SSE) were minimized. Present work revealed satisfactory agreement between experimental data and the result generated by complex ping-pong bi-bi model as compared to other models. The proposed kinetic model would facilitate understanding on enzymatic glycerolysis for DAG and MAG production and design optimization of a pilot-scale reactor.

Multi-Terahertz Sideband Generation on an Optical Telecom Carrier with a Quantum Cascade Laser

Quantum cascade lasers (QCLs) are the principal semiconductor light sources for the mid-infrared (MIR) and terahertz (THz) spectral regions. However, up-converting their emission to the technologically mature telecom spectral region (1.3 to 1.6 μm) remains an important goal for applications. This would permit new QCL functionalities to be realized, such as stabilization and injection locking of the QCL emission to precise and low-cost telecom frequency combs for spectroscopy. In this work, we demonstrate the up-conversion of the QCL emission to the telecom band at room temperature, using the QCLs’ inherent resonant optical nonlinearities that reduce the constraints of phase matching. This is based on the generation of multi-THz sidebands on a telecom carrier, where a low power telecom beam at 1.55 μm is injected into the cavity of an InP-based MIR QCL (9 μm, 33 THz), giving rise to the nonlinear sum frequency at 1.3 μm. The results are supported by a theoretical model that highlights the giant enhancement...

Localised detection of thiophenol with gold nanotriangles highly structured as honeycombs by nonlinear sum frequency generation spectroscopy

Gold nanotriangles structured as honeycombs and fabricated by nanosphere lithography on a gold film are functionalised by thiophenol molecules in order to be used as plasmonic sensors in nonlinear optical sum frequency generation (SFG) spectroscopy. The monitoring and the characterisation of the surface optical properties are performed by UV–visible differential reflectance spectroscopy showing an absorbance maximum located at 540 nm for p- and s-polarisation beams. SFG spectroscopy proves to be effective for thiophenol detection in ssp-polarisation scheme, while the molecular SFG signal disappears in ppp-configuration due to the strong s–d interband contribution of gold. However, in ssp-configuration, the vibration modes of thiophenol molecules at 3050 and 3071 $${\hbox {cm}}^{-1}$$ are yet observed thanks to the excitation of a transversal plasmon mode by the incident visible laser beam, whereas they are usually very difficult to distinguish by surface-enhanced Raman scattering and other vibrational optical probes.

Modelling of Asphalt Concrete Stiffness in the Linear Viscoelastic Region

Stiffness modulus is a fundamental parameter used in the modelling of the viscoelastic behaviour of bituminous mixtures. On the basis of the master curve in the linear viscoelasticity range, the mechanical properties of asphalt concrete at different loading times and temperatures can be predicted. This paper discusses the construction of master curves under rheological mathematical models i.e. the sigmoidal function model (MEPDG), the fractional model, and Bahia and co-workers’ model in comparison to the results from mechanistic rheological models i.e. the generalized Huet-Sayegh model, the generalized Maxwell model and the Burgers model. For the purposes of this analysis, the reference asphalt concrete mix (denoted as AC16W) intended for the binder coarse layer and for traffic category KR3 (5×105 <ESAL100kN <2.5×106) was prepared. Measurement of the stiffness modulus of asphalt concrete under steady-state strain was performed using the simple axial compression-tensile test under controlled strain mode. The fixed strain level was set at 25με to guarantee that the stiffness modulus of the asphalt concrete would be tested in a linear viscoelasticity range. The master curve was formed using the time-temperature superposition principle (TTSP). The stiffness modulus of asphalt concrete was determined at temperatures 10°C, 20°C and 40°C and at loading times (frequency) of 0.1, 0.3, 1, 3, 10, 20 Hz. The model parameters were fitted to the rheological models using the original programs based on the nonlinear least squares sum method. All the rheological models under analysis were found to be capable of predicting changes in the stiffness modulus of the reference asphalt concrete to satisfactory accuracy. In the cases of the fractional model and the generalized Maxwell model, their accuracy depends on a number of elements in series. The best fit was registered for Bahia and co-workers model, generalized Maxwell model and fractional model. As for predicting the phase angle parameter, the largest discrepancies between experimental and modelled results were obtained using the fractional model. Except the Burgers model, the model matching quality was more than 0.985 (determination coefficient) at the root mean squared error of less than 10%. From the point of view of their practical application, it is best to apply the generalized Huet-Sayegh model and the sigmoidal model.

Active Nonlinear Acoustic Sensing of an Object with Sum or Difference Frequency Fields

A number of nonlinear acoustic sensing methods exist or are being developed for diverse areas ranging from oceanic sensing of ecosystems, gas bubbles, and submerged objects to medical sensing of the human body. Our approach is to use primary frequency incident waves to generate second order nonlinear sum or difference frequency fields that carry information about an object to be sensed. Here we show that in general nonlinear sensing of an object, many complicated and potentially unexpected mechanisms can lead to sum or difference frequency fields. Some may contain desired information about the object, others may not, even when the intention is simply to probe an object by linear scattering of sum and difference frequency incident waves generated by a parametric array. Practical examples illustrating this in ocean, medical, air and solid earth sensing are given. To demonstrate this, a general and complete second-order theory of nonlinear acoustics in the presence of an object is derived and shown to be consistent with experimental measurements. The total second-order field occurs at sum or difference frequencies of the primary fields and naturally breaks into (A) nonlinear waves generated by wave-wave interactions, and (B) second order waves from scattering of incident wave-wave fields, boundary advection, and wave-force-induced centroidal motion. Wave-wave interactions are analytically shown to always dominate the total second-order field at sufficiently large range and carry only primary frequency response information about the object. As range decreases, the dominant mechanism is shown to vary with object size, object composition, and frequencies making it possible for sum or difference frequency response information about the object to be measured from second-order fields in many practical scenarios. It is also shown by analytic proof that there is no scattering of sound by sound outside the region of compact support intersection of finite-duration plane waves at sum or difference frequencies, to second-order. Analytic expressions for second-order fields due to combinations of planar and far-field wave-wave interactions are also derived as are conditions for when wave-wave interactions will dominate the second order field.

Stem taper and volume models for natural cedar and Taurus fir mixed stands in Bucak District

Abstract: In this study, we assessed the performance of different types of taper equations for predicting tree diameters at specific heights and total stem volumes for mixed stands of Taurus cedar ( Cedrus libani A. Rich.) and Taurus fir ( Abies cilicica Carr.). We used data from mixed stands containing a total of 131 cedar and 124 Taurus fir trees. We evaluated six commonly used and well-known forestry taper functions developed by a variety of researchers (Biging (1984), Zakrzewski (1999), Muhairwe (1999), Fang et al. (2000), Kozak (2004), and Sharma and Zhang (2004)). To address problems related to autocorrelation and multicollinearity in the hierarchical data associated with the construction of taper models, we used appropriate statistical procedures for the model fitting. We compared model performances based on the analysis of three goodness-of-fit statistics and found the compatible segmented model of Fang et al. (2000) to be superior in describing the stem profile and stem volume of both tree species in mixed stands. The equation used by Zakrzewski (1999) exhibited the poorest fitting results of the three taper equations. In general, we found segmented taper equations to provide more accurate predictions than variable-form models for both tree species. Results from the non-linear extra sum of squares method indicate that stem tapers differ among tree species in mixed stands. Therefore, a different taper function should be used for each tree species in mixed stands in the Bucak district. Using individual-specific taper equations yields more robust estimations and, therefore, will enhance the prediction accuracy of diameters at different heights and volumes in mixed stands. Keywords: Segmented model, compatible equation, stem form, merchantable volume, autocorrelation, F- test Received (Gelis): 08.02.2017 - Revised (Duzeltme): 17.03.2017 - Accepted (Kabul): 28.04.2017 Cite (Atif): Ozcelik, R., Dirican, O., 2017. Individual taper models for natural cedar and Taurus fir mixed stands of Bucak Region, Turkey. Journal of the Faculty of Forestry Istanbul University 67(2): 336-354. DOI: 10.17099/jffiu.290845

Modelos de volumen específicos y regionales para 12 especies forestales en el estado de Durango, México

Introduction: Estimating the volume of individual trees is an important aspect in dendrometry and in the conducting of forest inventories. Objective: Significant differences were evaluated in additive equation systems for estimating the total volume of individual trees in nine species of the genus Pinus (P. cooperi, P. durangensis, P. arizonica, P. leiophylla, P. teocote, P. engelmannii, P. lumholtzii, P. strobiformisand P. herrerae), and three of the genus Quercus (Q. sideroxyla, Q. durifoliaand Q. rugosa), and among regional forest management units (UMAFOR) when dealing with the same species. Materials and methods: To evaluate whether equation systems are different among tree species of the same genus and among the UMAFORs for the same species, two complementary statistical analyzes were used based on the fitting of a reduced and a full equation system: the F test of nonlinear extra sum of squares method, and the parameter significance analysis. Results and discussion: For most of the species studied, equation systems are significantly different. The need to use regional models in 10 of the 12 tree species, except for P. strobiformis and Q. rugosa, is also reported. Conclusion: The use of a state model for P. strobiformis and Q. rugosa is recommended.