Some new oscillation criteria of fourth-order quasi-linear differential equations with neutral term

In this article, we are interested in studying the asymptotic behavior of fourth-order neutral differential equations. Despite the growing interest in studying the oscillatory behavior of delay differential equations of second-order, fourth-order equations have received less attention. We get more than one criterion to check the oscillation by the generalized Riccati method and the integral average technique. Our results are an extension and complement to some results published in the literature. Examples are given to prove the significance of new theorems.

Symmetry and Its Role in Oscillation of Solutions of Third-Order Differential Equations

Symmetry plays an essential role in determining the correct methods for the oscillatory properties of solutions to differential equations. This paper examines some new oscillation criteria for unbounded solutions of third-order neutral differential equations of the form (r2(ς)((r1(ς)(z′(ς))β1)′)β2)′ + ∑i=1nqi(ς)xβ3(ϕi(ς))=0. New oscillation results are established by using generalized Riccati substitution, an integral average technique in the case of unbounded neutral coefficients. Examples are given to prove the significance of new theorems.

Qualitative Behavior of Unbounded Solutions of Neutral Differential Equations of Third-Order

New oscillatory properties for the oscillation of unbounded solutions to a class of third-order neutral differential equations with several deviating arguments are established. Several oscillation results are established by using generalized Riccati transformation and a integral average technique under the case of unbounded neutral coefficients. Examples are given to prove the significance of new theorems.

Analisis Kejadian El Nino dan Dampaknya Terhadap Musim Tanam dan Produktivitas Kacang Tanah (Arachis hypogaea L.) di Pulau Kei Kecil Kabupaten Maluku Tenggara

Climate change has an impact that includes extreme climate events such as El Nino. Experience in recent decades has shown that the El Nino climate anomaly has caused prolonged droughts. Peanut are susceptible to drought in part or all of its growth phases due to below-normal rainfall. This study aimed to describe the occurrence of extreme El-Nino rainfall on Kei Kecil Island, Maluku Province, and how much the El-Nino events affected the planting season and peanut production on Kei Kecil Island. This was carried out using the algebraic average technique for calculating the average (normal) rainfall and the FAO (1978) method for determining the growing season. The variables observed were rainfall data and peanut plant productivity data. Data were analyzed using simple regression analysis. The results of the study showed that the El Nino phenomenon generally took place in the period from April to November; mostly starting in April, May, June and September, October and November. Drought events on Kei Kecil Island did not always coincide with El Nino events, and El Nino events did not always cause drought or rainfall below normal. In 1993, 2003, 2007, and 2012 the amount of rainfall on Kei Kecil Island was below normal (<2,308 mm per year) but these years were not recorded as El Nino years. Whereas, 1994, 2009, 2014, and 2018 were recorded as El Nino years but did not cause drought or rainfall under normal conditions on Kei Kecil Island. During the last 30 years, this incident occurred 3 times, i.e. in 1991, 1997, and 2015. The results of the analysis of the growing season showed that the planting season on Kei Kecil Island under conditions of average (normal) rainfall lasted for 289 days or 9 months 16 days (November 1 to August 16). Meanwhile, the growing season when extreme El Nino rainfall occurred, lasted for 201 days or 6 months 20 days (November 1 to May 20). This indicated that when El Nino occurred on Kei Kecil Island, there was a shift in the growing season (ending sooner). The results of the regression analysis illustrated that the increase of the value of rainfall would increase the productivity of peanut crop. Keywords: El Nino phenomenon, growing season, peanut, productivity, rainfall ABSTRAK Perubahan iklim berdampak di antaranya terhadap kejadian iklim ekstrim seperti El Nino. Pengalaman dalam beberapa dekade terakhir ini menunjukkan bahwa anomali iklim El Nino telah menyebabkan kekeringan berkepanjangan. Kacang tanah rentan oleh deraan kekeringan pada sebagian ataupun seluruh fase pertumbuhannya akibat curah hujan yang di bawah normal. Penelitian ini bertujuan untuk mempelajari kejadian curah hujan ekstrim El-Nino di Pulau Kei Kecil, Provinsi Maluku, dan seberapa besar kejadian El-Nino mempengaruhi musim tanam dan produksi kacang tanah di Pulau Kei Kecil. Ini dilaksanakan dengan menggunakan metode teknik rata-rata aljabar untuk perhitungan curah hujan rata-rata (normal) dan metode FAO (1978) untuk penentuan musim tanam. Variabel yang diamati adalah data curah hujan dan data produktifitas tanaman kacang tanah. Data dianalisis menggunakan analisis regresi sederhana. Hasil penelitian menunjukkan fenomena El Nino umumnya berlangsung dalam periode April hingga November; terbanyak mulai bulan April, Mei, Juni dan September, Oktober dan November. Kejadian kekeringan di Pulau Kei Kecil tidak selalu bersamaan dengan kejadian El Nino, dan kejadian El Nino tidak selalu menyebabkan kekeringan atau curah hujan di bawah normal. Pada tahun 1993, 2003, 2007, dan 2012 jumlah curah hujan di Pulau Kei Kecil berada pada kondisi di bawah normal (<2.308 mm per btahun) tetapi tahun-tahun tersebut tidak tercatat sebagai tahun-tahun El Nino. Sementara itu, tahun 1994, 2009, 2014, dan 2018 tercatat sebagai tahun-tahun El Nino tetapi tidak menyebabkan kekeringan atau curah hujan di bawah kondisi normalnya di Pulau Kei Kecil. Selama periode 30 tahun terakhir kejadian ini berlangsung selama 3 kali, yaitu pada tahun 1991, 1997, dan 2015. Hasil analisis musim tanam menunjukkan bahwa musim tanam di Pulau Kei Kecil pada kondisi curah hujan rata-rata (normal) berlangsung selama 289 hari (1 November sampai dengan 16 Agustus; 9 bulan 16 hari). Sedangkan musim tanam ketika curah hujan ekstrim El Nino berlangsung selama 201 hari (1 November sampai dengan 20 Mei). Hal ini mengindikasikan bahwa ketika El Nino berlangsung di Pulau Kei Kecil, akan terjadi pergeseran musim tanam (berakhir lebih cepat). Hasil analisis regresi menggambarkan bahwa penigkatan nilai curah hujan akan menigkatkan produktivitas tanaman kacang tanah. Kata kunci: curah hujan, fenomena El Nino, kacang tanah, musim tanam, produktivitas

A New Model Averaging Approach in Predicting Credit Risk Default

The paper introduces a novel approach to ensemble modeling as a weighted model average technique. The proposed idea is prudent, simple to understand, and easy to implement compared to the Bayesian and frequentist approach. The paper provides both theoretical and empirical contributions for assessing credit risk (probability of default) effectively in a new way by creating an ensemble model as a weighted linear combination of machine learning models. The idea can be generalized to any classification problems in other domains where ensemble-type modeling is a subject of interest and is not limited to an unbalanced dataset or credit risk assessment. The results suggest a better forecasting performance compared to the single best well-known machine learning of parametric, non-parametric, and other ensemble models. The scope of our approach can be extended to any further improvement in estimating weights differently that may be beneficial to enhance the performance of the model average as a future research direction.

Time-domain signal averaging to improve microparticles detection and enumeration accuracy in a microfluidic impedance cytometer

Microfluidic impedance cytometry is a powerful system to measure micro and nano-sized particles and is routinely used in point-of-care settings disease diagnostics and other biomedical applications. However, small objects near a sensor’s detection limit are plagued with relatively significant background noise and are difficult to identify for every case. While many data processing techniques can be utilized to reduce noise and improve signal quality, frequently they are still inadequate to push sensor detection limits. Here, we report the first demonstration of a novel signal averaging algorithm effective in noise reduction of microfluidic impedance cytometry data, improving enumeration accuracy and reducing detection limits. Our device uses a 22 μm tall microchannel and gold coplanar microelectrodes that generates an electric field, recording bipolar pulses from polystyrene microparticles flowing through the channel. In addition to outlining a modified moving signal averaging technique theoretically and with a model dataset, we also performed a compendium of characterization experiments including variations in flow rate, input voltage, and particle size. Multi-variate metrics from each experiment are compared including signal amplitude, pulse width, background noise, and signal-to-noise ratio (SNR). Incorporating our technique resulted in improved SNR and counting accuracy across all experiments conducted, and the limit of detection improved from 5 μm to 1 μm particles without modifying microchannel dimensions. Succeeding this, we envision implementing our modified moving average technique to develop next generation microfluidic impedance cytometry devices with an expanded dynamic range and improved enumeration accuracy. This can be exceedingly useful for many biomedical applications, such as infectious disease diagnostics where devices may enumerate larger-scale immune cells alongside sub-micron bacterium in the same sample.

A technique to measure turbulent free convective heat transfer in a vertical tall cavity

A time-average technique was developed to measure the unsteady and turbulent free convection heat transfer in tall vertical enclosure using a Mach-Zehnder interferometer. The method used a digital high speed camera to obtain the time-averaged heat transfer rates. Optical heat transfer measurements were made in a differentially heated vertical cavity with isothermal walls. The cavity widths (distance between the plates) were L = 12.7, 32.3, 40, and 56.2 mm. The corresponding Rayleigh numbers were about 3X10[superscript] 3, 5 X 10⁴, 1 X 10⁵, 2.7. X 10⁵, respectively and the enclosure aspect ratio ranged from A=18 to 76. The test fluid was air and the temperature differential was about 15 K for all the measurements. Finite fringe interferograms were taken with a high speed camera. Interferograms of the fluctuating temperature field were captured for ten seconds at a frequency of 100Hz. These images were enhanced and processed using MATLAB to measure the local time-averaged heat transfer rate. This time-averaged heat flux was measured at many locations along the vertical cavity walls in order to obtain the spatial average. To validate the proposed technique, the average Nusselt number was compared to measured values and correlations from the literature. In both laminar and turbulent flow conditions, the current measurements compared well with the ElSherbiny correlation.

A technique to measure turbulent free convective heat transfer in a vertical tall cavity

A time-average technique was developed to measure the unsteady and turbulent free convection heat transfer in tall vertical enclosure using a Mach-Zehnder interferometer. The method used a digital high speed camera to obtain the time-averaged heat transfer rates. Optical heat transfer measurements were made in a differentially heated vertical cavity with isothermal walls. The cavity widths (distance between the plates) were L = 12.7, 32.3, 40, and 56.2 mm. The corresponding Rayleigh numbers were about 3X10[superscript] 3, 5 X 10⁴, 1 X 10⁵, 2.7. X 10⁵, respectively and the enclosure aspect ratio ranged from A=18 to 76. The test fluid was air and the temperature differential was about 15 K for all the measurements. Finite fringe interferograms were taken with a high speed camera. Interferograms of the fluctuating temperature field were captured for ten seconds at a frequency of 100Hz. These images were enhanced and processed using MATLAB to measure the local time-averaged heat transfer rate. This time-averaged heat flux was measured at many locations along the vertical cavity walls in order to obtain the spatial average. To validate the proposed technique, the average Nusselt number was compared to measured values and correlations from the literature. In both laminar and turbulent flow conditions, the current measurements compared well with the ElSherbiny correlation.

Simple regional analyses are still possible once correlated errors are removed

&lt;p&gt;Correlated errors in the monthly spherical harmonic coefficient (SHC) solutions provided by the GRACE data centers are estimated and removed using the destriping method of Crowley and Huang (2020). Regional estimates for mass change are calculated across Canada using the simple basin average technique of Swenson and Wahr (2002) as well as a simple mascon approach developed by the Canadian Geodetic Survey. A comparison with mascon solutions from the GRACE data centers demonstrates excellent agreement and in some cases reveals larger amplitudes and added temporal structure. This approach does not require additional constraints/dependencies, smoothing, normalizations or scaling factors and can easily be applied to any regional geometry without the need to calculate a global solution. Solutions tend to agree well when data quality is good and diverge when errors are larger. This is expected and demonstrates the underlying uncertainties that remain. The similarity in solutions using such different methodologies provides confidence in the time series solutions. We conclude with a regional validation that uses water level changes in the Great Lakes of North America to demonstrate the effectiveness of the method. The Great Lakes are large enough that GRACE clearly detects changes in their water levels. At the same time, the lakes are close enough to each other that distinguishing signals between adjacent lakes remains a challenge for any method.&lt;/p&gt;&lt;p&gt;References:&lt;/p&gt;&lt;p&gt;Crowley, J.W., and J Huang, A least-squares method for estimating the correlated error of GRACE models, Geophysical Journal International, Volume 221, Issue 3, June 2020, Pages 1736&amp;#8211;1749, https://doi.org/10.1093/gji/ggaa104.&lt;/p&gt;&lt;p&gt;Swenson, S., and J. Wahr, Methods for inferring regional surface-mass anomalies from Gravity Recovery and Climate Experiment (GRACE) measurements of time-variable gravity, J. Geophys. Res., 107(B9), 2193, doi:10.1029/2001JB000576, 2002.&lt;/p&gt;