Truncation Level Research Articles

Relationships between springs yield dynamics and hydrological drought development

This paper presents results of the identification and assessment of relationships between river discharge dynamics and spring yield during severe hydrological drought. The study covered a weekly yield series of eight springs and the daily discharge series of river gauging stations closing catchments including these springs. The investigated area was located in the mountainous, upper reaches of the Dunajec River basin (southern Poland) and the study covered the period 1989–2018. It was assumed that river low-flow is a good indicator of hydrological drought development. Severe streamflow droughts were estimated on the basis of the threshold level method (TLM) at a truncation level of 95% on the flow duration curve (FDC). Spring yield droughts were identified in the same way, however, there were three variants of truncation criteria. Synchronicity between both types of droughts was assessed on the basis of a co- occurrence ratio. To achieve the best fit criteria analysis, time shift steps of the spring yield series in relation to the river discharge series were conducted both for individual springs and for the whole investigated group. The best results of drought co-occurrence were achieved for the spring threshold at a multiannual average yield value, especially in backward and zero time shifts for fissure springs placed in relatively small catchments. Analysis of the course of relative spring drought intensity in following time shifts allowed an indication of the typical behaviours of the aquifer spring regime in relation to hydrological drought development.

Algebraic Varieties in Quantum Chemistry

AbstractWe develop algebraic geometry for coupled cluster (CC) theory of quantum many-body systems. The high-dimensional eigenvalue problems that encode the electronic Schrödinger equation are approximated by a hierarchy of polynomial systems at various levels of truncation. The exponential parametrization of the eigenstates gives rise to truncation varieties. These generalize Grassmannians in their Plücker embedding. We explain how to derive Hamiltonians, we offer a detailed study of truncation varieties and their CC degrees, and we present the state of the art in solving the CC equations.

Do Code Summarization Models Process Too Much Information? Function Signature May Be All That Is Needed

With the fast development of large software projects, automatic code summarization techniques, which summarize the main functionalities of a piece of code using natural languages as comments, play essential roles in helping developers understand and maintain large software projects. Many research efforts have been devoted to building automatic code summarization approaches. Typical code summarization approaches are based on deep learning models. They transform the task into a sequence-to-sequence task, which inputs source code and outputs summarizations in natural languages. All code summarization models impose different input size limits, such as 50 to 10,000, for the input source code. However, how the input size limit affects the performance of code summarization models still remains under-explored. In this article, we first conduct an empirical study to investigate the impacts of different input size limits on the quality of generated code comments. To our surprise, experiments on multiple models and datasets reveal that setting a low input size limit, such as 20, does not necessarily reduce the quality of generated comments. Based on this finding, we further propose to use function signatures instead of full source code to summarize the main functionalities first and then input the function signatures into code summarization models. Experiments and statistical results show that inputs with signatures are, on average, more than 2 percentage points better than inputs without signatures and thus demonstrate the effectiveness of involving function signatures in code summarization. We also invite programmers to do a questionnaire to evaluate the quality of code summaries generated by two inputs with different truncation levels. The results show that function signatures generate, on average, 9.2% more high-quality comments than full code.

Non-similar simulations of Ellis model based ternary hybrid nanofluid flow through porous media

The investigation of nanofluid flow through porous media is an emerging area of research in the optimization of thermal processing and numerous thermodynamic processes. The principal objective of these thermal applications is to examine the movement of ternary hybrid nanofluid across a stretched sheet oriented vertically. The flow being examined is represented mathematically in order to incorporate the influences of magnetic fields, thermal radiation, and viscous dissipation. The ternary hybrid nanofluid thermal performance can be enhanced and surpassed by adding nanoparticles to the base fluid. The non-Newtonian Ellis model takes into account the fluid movement through the porous media. Ferrous oxide ( Fe 3 O 4 ) , Zinc oxide ( ZnO ) , and Molybdenum disulfide ( Mo S 2 ) are regarded as nanoparticles, with ethylene glycol ( EG ) serving as the base fluid. To convert the governing equations into a dimensionless system, suitable non-similar transformations have been established. The local non-similarity (LNS) approach is used with the MATLAB built-in tool bvp4c up to the second truncation level. The physical impacts of dimensionless factors on the temperature and velocity profiles of the studied nanofluids are thoroughly investigated. When the magnetic and porosity parameters change, the velocity profile becomes smaller. The heat transmission rate declines when the assessments of the magnetic number and Eckert number increase. The skin friction coefficient experiences an increase as the estimates of magnetic properties and nanoparticle value rise. The current study holds various practical implications, encompassing Solar Thermal Energy Storage, Waste Heat Recovery, Advanced Cooling Technologies, Enhanced Geothermal Systems, and Enhanced Oil Recovery.

Regional and farm level droughts characteristics for southwestern Uganda during 1981–2017

An increase in drought events associated with rising temperatures indicates that Uganda is facing a growing challenge from climate variability. Despite these challenges, there is a lack of comprehensive information on how climate variability affects soils, particularly drought characteristics. In an effort to address this limitation, this study utilised high-quality, in-situ climate data and soil Available Water Capacity (AWC) specific to south-western Uganda. The study employed the Palmer Drought Severity Index (PDSI) and the Standardised Precipitation-Evapotranspiration Index (SPEI) to assess drought occurrences over the period 1981–2017. Notably, the results from the 3-month SPEI indicated higher frequencies across all drought categories. Meanwhile, the 12-month SPEI exhibited more stabilised negative and positive truncations for drought and wet events, respectively. Analysing the temporal evolution of monthly PDSI values for five major soil mapping units revealed distinct patterns. Moderate droughts were observed over Lixic Ferralsols between 1981 and 1992 and between 1998 and 2008. Extreme drought events occurred during the first 5–7 months of 2017. Luvisols exhibited prolonged negative truncation levels, indicating a water deficit during several periods: 1982–1984, 1990–1994, 1998–2000, 2010, and 2012–2014. Histosols experienced drought conditions from 1982 to 1986, interspersed with wet events in 1988, 1997, 1999–2002, and 2005. The study emphasises the differential response of soil units to drought and wet conditions. As a result, the research recommends implementing water management practices such as irrigation, mulching, conservation tillage, zero tillage, and drainage for all soils to enhance resilience and sustainable agricultural practices in the region.

Nonsimilar analysis of forced convection radially magnetized ternary hybrid nanofluid flow over a curved stretching surface

This study focuses on analyzing the rheological properties of the Carreau–Yasuda ternary hybrid nanofluid model on a curved stretched sheet considering the molybdenum disulfide ( Mo S 2 ) , graphene oxide ( GO ) , and Nichrome ( NiCr ) immersed in the base fluid ethylene glycol ( EG ) . This study employs a radial magnetic force that is directed perpendicular to the direction of flow to manipulate the motion characteristics of a nonNewtonian fluid. Augmenting the value of the magnetic number leads to a decrease in the velocity of the flow as resistance is introduced against its principal direction. Thermal radiation and viscous dissipation effects are considered in the energy equation. Assumptions that are fundamental to fluid flow theories are incorporated into the mathematical formulation of this problem. Following this, the governing equations are transformed into dimensionless nonsimilar partial differential equation (PDE) by applying nonsimilarity transformation to a nonsimilarity transformation, and subsequently analyzed as ordinary differential equations utilizing the local nonsimilarity method up to second level of truncation. By using the MATLAB-integrated bvp4c solver, numerical solutions are obtained. The results of these various solutions are examined using visual and tabular representations to thoroughly evaluate the variances across different parameter settings. Furthermore, the flow velocity is reduced by the Lorentz force caused by a more curved surface, and we gain insight into the impact of different physical quantities under different parametric considerations related to the stretching curved surface, which adds to our knowledge of this complex fluid dynamic phenomenon.

Entropy analysis of Hall effect with variable viscosity and slip conditions on rotating hybrid nanofluid flow over nonlinear radiative surface

PurposeWith possible uses in engineering and industrial processes, this work aims to further our knowledge of fluid dynamics and heat transfer in complicated flow configurations. This study looks at how Al2O3−Cu/H2O hybrid nanofluids move across a nonlinear radiative 3D unsteady surface. It tries to figure out what happens when the Hall current, variable viscosity, viscous dissipation, velocity and thermal slip conditions work together. The goal of this analysis is to provide insight into the system's thermodynamic behavior and the ways in which these elements affect the flow's entropy generation. MethodologyThe controlling system is converted into nonlinear nondimensional partial differential equations (PDEs) by applying suitable non-similar transformations. In this work, the governing equations are simulated using the local non-similarity (LNS) approach up to the second truncation level using the numerical technique bvp4c in MATLAB. FindingsThe temperature, velocity, entropy production, skin friction in both directions, and Nusselt number profiles of the nanofluid and hybrid nanofluid are detailed in many figures. The tabular form contains the results of computing the local Nusselt number for linear, nonlinear, and radiation-free scenarios. The velocity profiles in both directions and the temperature profile grow as the rotation parameter and nanoparticle volume fraction parameter increase. Conversely, the velocity profiles drop when the variable viscosity parameter falls, while the temperature profile increases. When the unsteadiness parameter A is set to 0.5 and the nanoparticle volume fraction is 1%, hybrid nanofluid has 4.26% lower x-direction skin friction than nanofluid and 3.62% greater y-direction friction. When the unsteadiness parameter A = 0.5 and the nanoparticle volume percentage is 1%, a hybrid nanofluid has a 2.77% higher Nusselt number than a nanofluid. The generation of entropy was also enhanced by an increase in the volume fraction of nanoparticles, radiation, temperature ratio, and Brinkman number. We evaluate and contrast the results of this study with those of earlier research.

Reduced-order modeling on a near-term quantum computer

Quantum computing is an advancing area of research in which computer hardware and algorithms are developed to take advantage of quantum mechanical phenomena. In recent studies, quantum algorithms have shown promise in solving linear systems of equations as well as systems of linear ordinary differential equations (ODEs) and partial differential equations (PDEs). Reduced-order modeling (ROM) algorithms for studying fluid dynamics have shown success in identifying linear operators that can describe flowfields, where dynamic mode decomposition (DMD) is a particularly useful method in which a linear operator is identified from data. In this work, DMD is reformulated as an optimization problem to propagate the state of the linearized dynamical system on a quantum computer. This reformulation was chosen as a means of facilitating implementation on a near-term quantum computer. Quadratic unconstrained binary optimization (QUBO), a technique for optimizing quadratic polynomials in binary variables, allows for quantum annealing algorithms to be applied. A quantum circuit model (quantum approximation optimization algorithm, QAOA) is utilized to obtain predictions of the state trajectories. Results are shown for the quantum-ROM predictions for flow over a 2D cylinder at Re = 220 and flow over a NACA0009 airfoil at Re = 500 and α=15∘. The quantum-ROM predictions are found to depend on the number of bits utilized for a fixed point representation and the truncation level of the DMD model. Comparisons with DMD predictions from a classical computer algorithm are made, as well as an analysis of the computational complexity and prospects for future, more fault-tolerant quantum computers.

A new hybrid GPU-CPU sparse LDLT factorization algorithm with GPU and CPU factorizing concurrently

This paper proposes a new task assignment scheme for sparse LDLT factorization on a hybrid GPU-CPU platform, and correspondingly an efficient supernodal algorithm, GPU Node and CPU Pipelining (GNCP). GNCP assigns a large number of weakly coupled tasks to GPU and CPU respectively so that GPU and CPU can execute different factorization tasks concurrently without explicit synchronization, which has not been achieved by previous researches. More precisely, based on the number of CPU threads, the global memory of GPU as well the size of the matrix, we introduce the concept of the truncation level in the partition tree built by the multi-level graph partitioning. The sum of FLOP associated with decoupled nodes in the truncation level accounts for about 65% of the whole computations in tested numerical examples. GNCP assigns the factorization tasks of each node in the truncation level to GPU. The data of each node in the truncation level are copied to the global memory of GPU and factorized entirely and independently by GPU one-by-one. Once factorization of any node in the truncation level has been completed, the cross-factorizations of this node to its ancestors and the following related operations are decoupled from other GPU tasks. These tasks are assigned to CPU threads with a reentrant pipelining strategy, accounting for about 35% of the whole calculations. Using this novel design, CPU and GPU are working concurrently and a large part of factorization is performed in overlapped time. Numerical tests for matrices from SuiteSparse matrix collection show higher performance than the well-known hybrid GPU-CPU solver CHOLMOD.

A generalized differential quadrature approach to the modelling of heat transfer in non-similar flow with nonlinear convection

This study aims to investigate heat transfer and entropy production in the non-similar flow of an incompressible fluid, with nonlinear convection and viscous dissipation. To obtain precise solutions, the Sparrow-Quack-Boerner local non-similarity method is implemented. The non-similarity arises from the nonlinear convection term present in the momentum equation. The non-similarity arises from the nonlinear convection term present in the momentum equation. Consequently, the inclusion of non-similarity terms into the energy equation is achieved through the interconnection of momentum and energy equations. Entropy generation is explored by employing the second law of thermodynamics. Numerical results from several truncation levels are presented in tabular form, and equations for both first and second-level truncations are generated. The one- and two-equation models are solved by implementing the Generalized Differential Quadrature Method (GDQM). Comparison with a second level of truncation reveals significantly greater inaccuracies in numerical results obtained from the first level. This discrepancy arose due to the omission of non-similar terms in the primary governing equations at the first truncation stage. The validity and accuracy of the derived numerical solutions are further demonstrated by the application of the GDQM and the midpoint method with Richardson extrapolation. Additionally, a plot of the numerical data produced from the second level of truncations is presented together with a discussion of the various physical factors. Increasing the mixed convection parameter accelerates fluid velocity, also when the viscous dissipation parameter increases, temperature and the Bejan number increase. The Prandtl number and the thickness of the thermal boundary layer are observed to be inversely related. Moreover, the quantity of entropy generated at the stretching surface and inside the boundary layer rises in proportion to the increases in the Prandtl and Eckert numbers.

Non-similar analysis of radially magnetized flow and heat transfer of Reiner–Philippoff based nanofluid over a curved stretching surface with viscous dissipation

The aim of this study is to conduct a non-similar analysis of flow and heat transfer rheology of non-Newtonian fluid over a radially magnetized curved stretching surface in the presence of multiple type of nanoparticles. Reiner–Philippoff viscosity and homogenous models are incorporated in the governing equation to study the effects of non-Newtonian fluid and nanoparticles respectively. Reiner–Philippoff viscosity model is a complicated non-Newtonian fluid model presenting an implicit stress-strain relationship. This fluid model has ability to present viscosity behavior in response to varying viscoelastic conditions of shear-thinning, shear-thickening as well as Newtonian fluid. The nanoparticles of nickel, molybdenum disulfide, and tantalum are used to study the enhancement of the thermal conductivity of the fluid with influences of radiative heat flux and viscous dissipation. To attain a more precise and generalized analysis of the heat transfer and flow, the governing boundary layer equations are converted to non-similar form. The local non-similarity method up to second level of truncation is employed to numerically solve the resulting non-similar PDEs via bvp4c in MATLAB tools. To examine the impact of physical factors on flow and heat transfer, numerical data are visually and tabulated displayed. It is worth mentioning that the thermal radiation, curvature parameter, and magnetic number play important role in controlling wall drag and heat flux.

Improvement of non-integrated defect relation for meromorphic maps from Kähler manifolds

ABSTRACT The purpose of this paper is to establish a non-integrated defect relation for meromorphic mappings from a complete Kähler manifold into a projective variety intersecting an arbitrary family of hypersurfaces with explicit truncation level. In our result, both the total defect and the truncation level are estimated independently of the number of involved hypersurfaces. Our result generalizes and improves the previous results in this topic.

Non-similar bioconvective analysis of magnetized hybrid nanofluid (Ag + TiO2) flow over exponential stretching surface

Scientists have studied fluid flow over a stretching sheet to explore its potential applications in industries. This study investigates the exponential stretching flow of a bioconvective magnetohydrodynamic (MHD) hybrid nanofluid in porous medium taking into consideration thermal radiations, heat generation, chemical reaction, porosity, and dissipation. Moreover, microorganisms are present in the fluid, so the fluid is more stable, which is crucial in biotechnology, biomicrosystems, and bio-nano coolant systems. Silver and titanium dioxide in a water-based medium are the prototypical nanoparticles. The present study involves a transformation of the governing system into a set of dimensionless, coupled and nonlinear partial differential equations (PDEs) using nonsimilar techniques. The local non-similarity (LNS) technique is used to truncate these equations to ordinary differential equations (ODEs). This technique is also used to estimate transformed equations numerically until the second level of truncation takes place via the bvp4c algorithm, which is a built-in MATLAB solver. Furthermore, tables are provided that presents the drag coefficients, Nusselt numbers, Sherwood numbers, and densities of motile microorganisms. Results show a negative correlation between the velocity and the magnetic field parameter as well as the porosity parameter, as evidenced by a decrease in velocity corresponds to rises in these parameters. The temperature distribution exhibits a positive correlation with the rising values of both radiation parameter and Eckert number. The concentration profiles also exhibit a negative correlation with the increasing values of Lewis and bioconvection Lewis number, chemical reaction parameter, Peclet number and the differences in microbial concentration. This study will improve the future research on hybrid nanofluid regarding industrial applications. There haven't been any previous publications that have investigated the use of this model with the local non-similarity method. The main objective of this article is to enhance the heat transfer performance in a hybrid nanofluid.

An Early Iron Age Roundhouse at Gartness Road, Drymen, Stirling

An archaeological excavation at Gartness Road Drymen, undertaken by Headland Archaeology (UK) Ltd in 2020, revealed the remains of an early Iron Age roundhouse and a small collection of pits. The remains exhibited a high level of truncation, which obscured the potentially complex nature of the structure. The site was located on the south-eastern edge of Loch Lomond and the Trossachs National Park, an area which sits on the traditional highland to lowland boundary. This unique location and early date for the structure provided an opportunity to explore construction styles, potentially contemporary activity and its relationship to surrounding structures.

Current State of Advances in Quantification and Modeling of Hydrological Droughts

Hydrological droughts may be referred to as sustained and regionally extensive water shortages as reflected in streamflows that are noticeable and gauged worldwide. Hydrological droughts are largely analyzed using the truncation level approach to represent the desired flow condition such as the median, mean, or any other flow quantile of an annual, monthly, or weekly flow sequence. The quantification of hydrologic droughts is accomplished through indices, such as the standardized streamflow index (SSI) in tandem with the standardized precipitation index (SPI) commonly used in meteorological droughts. The runs of deficits in the SSI sequence below the truncation level are treated as drought episodes, and thus, the theory of runs forms an essential tool for analysis. The parameters of significance from the modeling perspective of hydrological droughts (or tantamount to streamflow droughts in this paper) are the longest duration and the largest magnitude over a desired return period of T-year (or month or week) of the streamflow sequences. It is to be stressed that the magnitude component of the hydrological drought is of paramount importance for the design and operation of water resource storage systems such as reservoirs. The time scales chosen for the hydrologic drought analysis range from daily to annual, but for most applications, a monthly scale is deemed appropriate. For modeling the aforesaid parameters, several methodologies are in vogue, i.e., the empirical fitting of the historical drought sequences through a known probability density function (pdf), extreme number theorem, Markov chain analysis, log-linear, copulas, entropy-based analyses, and machine learning (ML)-based methods such as artificial neural networks (ANN), wavelet transform (WT), support vector machines (SVM), adaptive neuro-fuzzy inference systems (ANFIS), and hybrid methods involving entropy, copulas, and machine learning-based methods. The forecasting of the hydrologic drought is rigorously conducted through machine learning-based methodologies. However, the traditional stochastic methods such as autoregressive integrated moving average (ARIMA), seasonal autoregressive integrated moving average (SARIMA), copulas, and entropy-based methods are still popular. New techniques for flow simulation are based on copula and entropy-based concepts and machine learning methodologies such as ANN, WT, SVM, etc. The simulated flows could be used for deriving drought parameters in consonance with traditional Monte Carlo methods of data generation. Efforts are underway to use hydrologic drought models for reservoir sizing across rivers. The ML methods whilst combined in the hybrid form hold promise in drought forecasting for better management of existing water resources during the drought periods. Data mining and pre-processing techniques are expected to play a significant role in hydrologic drought modeling and forecasting in future.

Nonsimilar analysis of ternary hybrid Eyring–Powell nanofluid flow over a linearly stretching surface

Purpose This study investigates the flow and heat transfer in a magnetohydrodynamic (MHD) ternary hybrid nanofluid (HNF), considering the effects of viscous dissipation and radiation.Design/methodology/approach The transport equations are transformed into nondimensional partial differential equations. The local nonsimilarity (LNS) technique is implemented to truncate nonsimilar dimensionless system. The LNS truncated equation can be treated as ordinary differential equations. The numerical results of the equation are accomplished through the implementation of the bvp4c solver, which leverages the fourth-order three-stage Lobatto IIIa formula as a finite difference scheme.Findings The findings of a comparative investigation carried out under diverse physical limitations demonstrate that ternary HNFs exhibit remarkably elevated thermal efficiency in contrast to conventional nanofluids.Originality/value The LNS approach (Mahesh et al., 2023; Khan et al., 20223; Farooq et al., 2023) that we have proposed is not currently being used to clarify the dynamical issue of HNF via porous media. The LNS method, in conjunction with the bvp4c up to its second truncation level, yields numerical solutions to nonlinear-coupled PDEs. Relevant results of the topic at hand, obtained by adjusting the appropriate parameters, are explained and shown visually via tables and diagrams.

An Empirical Analysis of the Effect of Ballot Truncation on Ranked-Choice Electoral Outcomes

In ranked-choice elections voters cast preference ballots which provide a voter's ranking of the candidates. The method of ranked-choice voting (RCV) chooses a winner by using voter preferences to simulate a series of runoff elections. Some jurisdictions which use RCV limit the number of candidates that voters can rank on the ballot, imposing what we term a truncation level, which is the number of candidates that voters are allowed to rank. Given fixed voter preferences, the winner of the election can change if we impose different truncation levels. We use a database of 1183 real-world ranked-choice elections to empirically analyze the potential effects of imposing different truncation levels in ranked-choice elections. Our general finding is that if the truncation level is at least three then restricting the number of candidates on the ballot rarely affects the election winner.

Analysis of mixed convective stagnation point flow of hybrid nanofluid over sheet with variable thermal conductivity and slip Conditions: A Model-Based study

This research looks at the stagnation point flow of MHD Al2O3-Cu/H2O hybrid nanofluid against a permeable, vertically extending surface that uses thermal radiation and how different models of thermal conductivity affect it. This study is unique because it looks at how changes in thermal conductivity, mixed convection, and the slip velocity of hybrid nanofluids affect the stretching surface. It also looks at how changes in temperature, skin-friction coefficient, Nusselt number, and velocity affect convective thermal boundary conditions. With the use of boundary layer approximations, the complicated system of PDEs is simplified. The dimensionality of these PDEs and the boundary conditions they include are eliminated by applying certain modifications. Combining a local non-similarity approach up to the second truncation level with MATLAB's built-in finite difference code (bvp4c), one can obtain the results of the updated model. The research demonstrates and analyzes the impact of different factors on fluid flow and heat transfer characteristics in the studied flow situations. This is done by comparing the computed data with available literature and presenting the findings in graphical form. Tables are generated to present the numerical fluctuations of the drag coefficient and Nusselt number. This study shows how important thermal conductivity is in the mixed convection of hybrid nanofluids and looks into what happens when the thermal conductivity parameter is changed. Significantly, an augmentation in this parameter results in an elevation in the temperature distribution of the hybrid nanofluid while simultaneously reducing the rate of heat transfer across various models. Furthermore, increasing the nanoparticle volume fraction parameter leads to higher temperature and Nusselt number profiles while reducing skin friction. The mixed convection parameter has a notable impact on increasing the friction coefficient on the stretched vertical surface. However, because these elements function as regulating variables, it decreases when the magnetic, mass suction, and velocity slip parameters are present. The results also demonstrate notable discrepancies in the mean Nusselt values generated by various thermal conductivity models. According to the analysis, the Hamilton-Crosser model has the lowest average Nusselt numbers, followed by the Yamada-Ota model and the Xue model, in that order.

Existence of large-data global weak solutions to kinetic models of nonhomogeneous dilute polymeric fluids

We prove the existence of large-data global-in-time weak solutions to a general class of coupled bead-spring chain models with finitely extensible nonlinear elastic (FENE) type spring potentials for nonhomogeneous incompressible dilute polymeric fluids in a bounded domain in $ \mathbb{R}^d $, $ d = 2 $ or $ 3 $. The class of models under consideration involves the Navier–Stokes system with variable density, where the viscosity coefficient depends on both the density and the polymer number density, coupled to a Fokker–Planck equation with a density-dependent drag coefficient. The proof is based on combining a truncation of the probability density function with a two-stage Galerkin approximation and weak compactness and compensated compactness techniques to pass to the limits in the sequence of Galerkin approximations and in the truncation level.

Second main theorem for holomorphic curves on annuli with arbitrary families of hypersurfaces

<abstract><p>The aim of this paper is to establish the second main theorem for holomorphic curves from the annulus into a complex projective variety intersecting an arbitrary family of hypersurfaces. This is done by using the notion of "Distributive Constant" for a family of hypersurfaces with respect to a complex projective variety developed by Quang. We also give an explicit estimate for the level of truncation.</p></abstract>