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Isolation And Assessment Of Halophilic Rhizobacteria Plant Growth-Promoting Traits For Alleviating Salt Stress In Wheat, Alev Sezen, Ömer Faruk Algur, Ferruh Aşçi, Arzu Ünal Mar 2024

Isolation And Assessment Of Halophilic Rhizobacteria Plant Growth-Promoting Traits For Alleviating Salt Stress In Wheat, Alev Sezen, Ömer Faruk Algur, Ferruh Aşçi, Arzu Ünal

Turkish Journal of Botany

In this study, 22 halophilic bacteria were isolated from plants collected together with rhizosphere soil from habitats with high salt content in and around Erzurum. Various plant growth-promoting (PGP) properties of these isolates (nitrogen fixing, phosphate solubilizing, ACC deaminase, and IAA and siderephore production) were determined. Bacteria positive for PGP properties and various combinations with these bacteria were subjected to pot experiments in saline medium (greenhouse conditions) and their effects on growth parameters (root and stem length, fresh and dry weight, protein, and chlorophyll and carotenoid content) of wheat plants were determined. As a result of the research, the isolates …


A New Fossil Wood Species Of Ziziphus From The Middle Miocene Of Türkiye And Its Palaeoenvironmental Evaluation, Ünal Akkemi̇k, Özlem Toprak Mar 2024

A New Fossil Wood Species Of Ziziphus From The Middle Miocene Of Türkiye And Its Palaeoenvironmental Evaluation, Ünal Akkemi̇k, Özlem Toprak

Turkish Journal of Botany

The purpose of this study is to describe a new fossil wood from the Middle Miocene of South Anatolia (Mersin) and to identify it and evaluate its palaeoenvironmental implications. Thin sections of transverse, tangential, and radial surfaces were examined and described using the terminology of the International Association of Wood Anatomists. The wood was determined to have characteristics of Ziziphus (Rhamnaceae). It is the first fossil wood of Ziziphus and is described as Ziziphoxylon sayaz Akkemik sp. nov. It is from the Middle Miocene Climate Optimum (MMCO), which is a relatively warm interval in the Miocene. Indistinct annual growth ring …


A New Permineralized Corypha-Type Coryphoid Palm Stem From K-Pg Of India: Anatomy, Systematics, Saprophytic Fungi, And Paleoecology, Ashif Ali, Kaustav Roy, Biswajit Mukherjee, Subir Bera, Mahasin Khan Mar 2024

A New Permineralized Corypha-Type Coryphoid Palm Stem From K-Pg Of India: Anatomy, Systematics, Saprophytic Fungi, And Paleoecology, Ashif Ali, Kaustav Roy, Biswajit Mukherjee, Subir Bera, Mahasin Khan

Turkish Journal of Botany

Palms are known to be an important and diverse angiosperm component in the Deccan Intertrappean beds of Central India. However, the report of fossilized palm stems inhibiting saprophytic fungal remains is empty in the field of paleobotany. Here, we document for the first time the occurrence of fungal remains in a petrified palm stem collected from the latest Maastrichtian (Late Cretaceous)-earliest Danian (early Paleocene) sediments of the Deccan Intertrappean beds of Madhya Pradesh, Central India. The anatomical features of the fossil stem are characterized by the presence of Corypha-type general stem pattern (progressive decrease of fibrous parts of fibrovascular bundles, …


A Two-Stage Deformation Of The Anatolian Plate Deduced From Paleomagnetic Signals: The Initial Age Of The Anatolian’S Escape, Mualla Cengi̇z, Savaş Karabulut Mar 2024

A Two-Stage Deformation Of The Anatolian Plate Deduced From Paleomagnetic Signals: The Initial Age Of The Anatolian’S Escape, Mualla Cengi̇z, Savaş Karabulut

Turkish Journal of Earth Sciences

The Neotectonic period of deformation in Anatolia has been embraced by a location between the complex interaction of Afro-Arabian and Eurasia plates. During this ongoing deformation, the eastern part was under the continuing influence of subduction by the Neotethyan Ocean in the Eastern Mediterranean Region resulting in the indentation of the Arabian Plate into Anatolia. As the Red Sea opened deformation became increasingly focused on a fault system comprising the Dead Sea, North Anatolian, and East Anatolian fault systems. To help constrain the age and deformation history of this last phase we have conducted a paleomagnetic study from a total …


Petrological And Geochemical Constraints On Provenance, Paleoweathering, And Tectonic Setting Of The Cambro-Ordovician Khabour Formation, Western And Northern Iraq, Ali I. Al Juboury, Muhamed F. Omer, Mohammed A. Al-Haj, Stephen J. Vincent, James P. Howard, Gary Nichols, Benoit Vautravers Mar 2024

Petrological And Geochemical Constraints On Provenance, Paleoweathering, And Tectonic Setting Of The Cambro-Ordovician Khabour Formation, Western And Northern Iraq, Ali I. Al Juboury, Muhamed F. Omer, Mohammed A. Al-Haj, Stephen J. Vincent, James P. Howard, Gary Nichols, Benoit Vautravers

Turkish Journal of Earth Sciences

Petrographic descriptions and point counting data, supported by SEM analysis, are presented for 89 sandstone samples of the Khabour Formation from the Khabour, Ora, Chalki Nasara, and Chia Zinnar outcrop sections in northern Iraq. These are compared with previously published data for subsurface samples from the Akkas-1 and Akkas-3 wells in western Iraq. Petrographic observations revealed that sublitharenites and subarkoses form the main sandstone types and may suggest a granitic source region with minor input from metamorphosed sediments. This is supported by the geochemical analysis gained from 66 sandstone samples. Chemical Index of Alteration (CIA) and Index of Chemical Variability …


Örenli Metamorphics (Biga Peninsula, Nw Anatolia): Evidence For Triassic Active Continental Margin Of Paleo-Tethys Ocean, İsmai̇l Onur Tunç Mar 2024

Örenli Metamorphics (Biga Peninsula, Nw Anatolia): Evidence For Triassic Active Continental Margin Of Paleo-Tethys Ocean, İsmai̇l Onur Tunç

Turkish Journal of Earth Sciences

The pre-Liassic basement of the Biga Peninsula, located in the westernmost part of the Sakarya Zone, consists of metamorphic assemblages that were considered to represent different continental basements in the north and south, and the suture (ophiolitic/mélange) zone(s) between them. The Çetmi mélange, defined as between these continental fragments (the Kazdağ Massif in the south and the Çamlıca Massif in the north) was evaluated as a subduction accretionary mélange of the Intra-Pontide Ocean and it was assumed that a suture passed through this part of the peninsula. This study was carried out on the most widely distributed outcrops of the …


A Deep Insight Into A Chemically Homogeneous Banded Pumice Sample: A Role Of Crystal Cargo Immiscibility, Lütfi̇ye Akin, Erkan Aydar, Abdullah Ceylan Mar 2024

A Deep Insight Into A Chemically Homogeneous Banded Pumice Sample: A Role Of Crystal Cargo Immiscibility, Lütfi̇ye Akin, Erkan Aydar, Abdullah Ceylan

Turkish Journal of Earth Sciences

In this study, a set of representative banded rhyolitic pumice xenoliths collected from the ejecta of a basaltic cinder cone around Göllüdağ volcanic center, Central Anatolia, Türkiye, were characterized through whole-rock and mineral analyses, scanning electron microscopy (SEM), microcomputed tomography (µ-CT), and magnetization studies. The light- and dark-colored bands exhibit similar whole-rock chemistry, mainly distributed in rhyolite composition (71.35–71.66 wt.% SiO2). The dark pumice band shows high crystallinity (12–14 vol.%) with abundant subhedral-euhedral phenocrystals, microphenocrystals, and microlites, and a glass composition consisting of 71–76 wt.% SiO2. In contrast, the light pumice band exhibits relatively low crystallinity (1.86–8.08 vol.%) with phenocrystals …


Coastal Discharge Extremes And Their Environmental Impact On The Sea Of Marmara, Nüvi̇t Berkay Başdurak Mar 2024

Coastal Discharge Extremes And Their Environmental Impact On The Sea Of Marmara, Nüvi̇t Berkay Başdurak

Turkish Journal of Earth Sciences

Increases in evaporation driven by global warming change the hydrological cycle by fueling extreme precipitation and exacerbating the frequency and intensity of extreme floods. Combined with the increase in terrestrial waste and pollutants, the changing climate exposes coastal zones to natural hazards. The Sea of Marmara, as an inland sea with a dense coastal population, is more vulnerable to such changes and subject to eutrophication and extreme environmental events (e.g., mucilage). Therefore, quantification of daily and along-coast variation of river discharge and evaluation of its annual trend of extremes are crucial. The daily discharges from the coastal watersheds Biga, Gönen, …


Dorycnium Vuralii (Fabaceae), A New Species From Türkiye, Bilal Şahi̇n, Seher Karaman, Mevlüde Alev Ateş, Zeki Aytaç Mar 2024

Dorycnium Vuralii (Fabaceae), A New Species From Türkiye, Bilal Şahi̇n, Seher Karaman, Mevlüde Alev Ateş, Zeki Aytaç

Turkish Journal of Botany

The present study describes a new species Dorycnium vuralii (Fabaceae) from Çankırı, Türkiye. The new species is compared morphologically to the taxa of sect. Bonjeanea and sect. Dorycnium along with pollen micromorphology, leaflet, and seed micromorphology. The geographical distribution of Dorycnium vuralii is mapped. The phylogenetic relationships between the new species and other closely related species in the genus are inferred based on DNA data from both cpDNA and nrDNA (rbcL1&ITS). Although phylogenetic implications are different in the two DNA barcoding regions, D. vuralii is shown to be a new species in both molecular data. The new species is assessed …


Cover And Contents Mar 2024

Cover And Contents

Turkish Journal of Electrical Engineering and Computer Sciences

No abstract provided.


Intelligent Protection Scheme Using Combined Stockwell-Transform And Deep Learning-Based Fault Diagnosis For The Active Distribution System, Latha Maheswari Kandasamy, Kanakaraj Jaganathan Mar 2024

Intelligent Protection Scheme Using Combined Stockwell-Transform And Deep Learning-Based Fault Diagnosis For The Active Distribution System, Latha Maheswari Kandasamy, Kanakaraj Jaganathan

Turkish Journal of Electrical Engineering and Computer Sciences

This study aims to perform fast fault diagnosis and intelligent protection in an active distribution network (ADN) with high renewable energy penetration. Several time-domain simulations are carried out in EMTP-RV to extract time-synchronized current and voltage data. The Stockwell transform (ST) was used in MATLAB/SIMULINK to preprocess these input datasets to train the adaptive fault diagnosis deep convolutional neural network (AFDDCNN) for fault location identification, fault type identification, and fault phase-detection for different penetration levels. Based on the AFDDCNN output, the intelligent protection scheme (IDOCPS) generates the signal for isolating a faulty section of the ADN. An intelligent fault diagnosis …


Advanced Hyperthermia Treatment: Optimizing Microwave Energy Focus For Breast Cancer Therapy, Burak Acar, Tuba Yilmaz Abdolsaheb, Ali Yapar Mar 2024

Advanced Hyperthermia Treatment: Optimizing Microwave Energy Focus For Breast Cancer Therapy, Burak Acar, Tuba Yilmaz Abdolsaheb, Ali Yapar

Turkish Journal of Electrical Engineering and Computer Sciences

This paper presents a fast antenna phase optimization scheme to enable microwave power focusing for breast cancer hyperthermia. The power focusing is achieved through the maximization of the deposited electric field on the target malignant tumor tissue. To do so, a malignant breast tumor, the surrounding breast medium, and the skin of the breast are modeled as a cylindrical structure composed of eccentric cylinders, and electric field distribution is computed analytically in terms of cylindrical harmonics. This approach minimized the computational cost and simplified the breast medium model. To ensure applicability across various breast types, the dielectric properties (DPs) of …


Atomic Comagnetometer Gyroscopes For Inertial Navigation Systems: A Review, Murat Salim Karabinaoglu, Bekir Çakir, Mustafa Engin Başoğlu Mar 2024

Atomic Comagnetometer Gyroscopes For Inertial Navigation Systems: A Review, Murat Salim Karabinaoglu, Bekir Çakir, Mustafa Engin Başoğlu

Turkish Journal of Electrical Engineering and Computer Sciences

In recent years, developments in quantum sensing, laser, and atomic sensor technologies have also enabled advancement in the field of quantum navigation. Atomic-based gyroscopes have emerged as one of the most critical atomic sensors in this respect. In this review, a brief technology statement of spin exchange relaxation free (SERF) and nuclear magnetic resonance (NMR) type atomic comagnetometer gyroscope (CG) is presented. Related studies in the literature have been gathered, and the fundamental compositions of CGs with technical basics are presented. A comparison of SERF and NMR CGs is provided. A basic simulation of SERF CG was carried out because …


Uncovering And Mitigating Spurious Features In Domain Generalization, Saeed Karimi, Hamdi̇ Di̇bekli̇oğlu Mar 2024

Uncovering And Mitigating Spurious Features In Domain Generalization, Saeed Karimi, Hamdi̇ Di̇bekli̇oğlu

Turkish Journal of Electrical Engineering and Computer Sciences

Domain generalization (DG) techniques strive to attain the ability to generalize to an unfamiliar target domain solely based on training data originating from the source domains. Despite the increasing attention given to learning from multiple training domains through the application of various forms of invariance across those domains, the enhancements observed in comparison to ERM are nearly insignificant under specified evaluation rules. In this paper, we demonstrate that the disentanglement of spurious and invariant features is a challenging task in conventional training since ERM simply minimizes the loss and does not exploit invariance among domains. To address this issue, we …


Lower Data Attacks On Advanced Encryption Standard, Orhun Kara Mar 2024

Lower Data Attacks On Advanced Encryption Standard, Orhun Kara

Turkish Journal of Electrical Engineering and Computer Sciences

The Advanced Encryption Standard (AES) is one of the most commonly used and analyzed encryption algorithms. In this work, we present new combinations of some prominent attacks on AES, achieving new records in data requirements among attacks, utilizing only 2 4 and 2 16 chosen plaintexts (CP) for 6-round and 7-round AES 192/256, respectively. One of our attacks is a combination of a meet-in-the-middle (MiTM) attack with a square attack mounted on 6-round AES-192/256 while another attack combines an MiTM attack and an integral attack, utilizing key space partitioning technique, on 7-round AES-192/256. Moreover, we illustrate that impossible differential (ID) …


Consensus-Based Virtual Leader Tracking Algorithm For Flight Formation Control Of Swarm Uavs, Berat Yıldız, Akif Durdu, Ahmet Kayabaşi Mar 2024

Consensus-Based Virtual Leader Tracking Algorithm For Flight Formation Control Of Swarm Uavs, Berat Yıldız, Akif Durdu, Ahmet Kayabaşi

Turkish Journal of Electrical Engineering and Computer Sciences

Technological developments in industrial areas also impact unmanned aerial vehicles (UAVs). Recent improvements in both software and hardware have significantly increased the use of many UAVs in social and military fields. In particular, the widespread use of these vehicles in social areas such as entertainment, shipping, transportation, and delivery and military areas such as surveillance, tracking, and offensive measures has accelerated the research on swarm systems. This study examined the previous investigations on swarm UAVs and aimed to create a more efficient algorithm. The effectiveness of the proposed algorithm was compared with other leader-based applications. A swarm consisting of 5 …


Cascade Controller Design Via Controller Synthesis For Load Frequency Control Of Electrical Power Systems, Yavuz Güler, Mustafa Nalbantoğlu, Ibrahim Kaya Mar 2024

Cascade Controller Design Via Controller Synthesis For Load Frequency Control Of Electrical Power Systems, Yavuz Güler, Mustafa Nalbantoğlu, Ibrahim Kaya

Turkish Journal of Electrical Engineering and Computer Sciences

The regulation of tie-line electricity flow and frequency of electrical power systems (EPS) is crucial for ensuring their robustness to parameter changes and efficient management of disturbances. To this end, a novel cascade control design approach utilizing a serial Proportional-Integral-Derivative controller with a filter (PIDF) is proposed in this paper. The parameters of the controllers are derived analytically, and it is employed in both loops of the cascade control system to regulate the Load Frequency Control (LFC) of EPS. The implementation of PIDF controllers in both loops is utilized in the cascade control scheme for various power systems featuring different …


Cover And Contents Mar 2024

Cover And Contents

Turkish Journal of Mathematics

No abstract provided.


Fusion In Supersolvable Hall Subgroups, Muhammet Yasi̇r Kizmaz Mar 2024

Fusion In Supersolvable Hall Subgroups, Muhammet Yasi̇r Kizmaz

Turkish Journal of Mathematics

Let H be a supersolvable Hall π -subgroup of a finite group G. We prove that G has a normal π -complement if and only if H controls G-fusion in H.


Twisted Sasaki Metric On The Unit Tangent Bundle And Harmonicity, Liana Lotarets Mar 2024

Twisted Sasaki Metric On The Unit Tangent Bundle And Harmonicity, Liana Lotarets

Turkish Journal of Mathematics

The paper deals with the twisted Sasaki metric on the unit tangent bundle of n–dimensional Riemannian manifold Mn . The main purpose of the research is to find deformations that preserve the existence harmonic left-invariant unit vector fields on 3-dimensional unimodular Lie groups G with the left invariant metric and harmonic maps G → T1G in case of twisted Sasaki metric on the unit tangent bundle. The necessary and sufficient conditions for harmonicity of left-invariant unit vector field and map Mn → T1Mn are obtained. The necessary and sufficient conditions for harmonicity of left-invariant unit vector field and map M2 …


Langevin Delayed Equations With Prabhakar Derivatives Involving Two Generalized Fractional Distinct Orders, Mustafa Aydin Mar 2024

Langevin Delayed Equations With Prabhakar Derivatives Involving Two Generalized Fractional Distinct Orders, Mustafa Aydin

Turkish Journal of Mathematics

This paper is devoted to defining the delayed analogue of the Mittag-Leffler type function with three parameters and investigating a representation of a solution to Langevin delayed equations with Prabhakar derivatives involving two generalized fractional distinct orders, which are first introduced and investigated, by means of the Laplace integral transform. It is verified by showing the solution satisfies the introduced system. Special cases which are also novel are presented as examples. The findings are illustrated with the help of the RLC circuits.


Combinatorial Results For Semigroups Of Orientation-Preserving Transformations, Ayşegül Dağdevi̇ren, Gonca Ayik Mar 2024

Combinatorial Results For Semigroups Of Orientation-Preserving Transformations, Ayşegül Dağdevi̇ren, Gonca Ayik

Turkish Journal of Mathematics

Let Xn denote the chain {1, 2, . . . , n} under its natural order. We denote the semigroups consisting of all order-preserving transformations and all orientation-preserving transformations on Xn by On and OPn , respectively. We denote by E(U) the set of all idempotents of a subset U of a semigroup S . In this paper, we first determine the cardinalities of Er(On) = {α ∈ E(On) : |im(α)| = |fix(α)| = r}, E ∗ r (On) = {α ∈ Er(On) : 1, n ∈ fix(α)}, Er(OPn) = {α ∈ E(OPn) : |fix(α)| = r}, E ∗ r …


On The Reconstruction Of An Integro-Differential Dirac Operator With Parameter-Dependent Nonlocal Integral Boundary Conditions From The Nodal Data, Baki Keskin, Yu Ping Wang Mar 2024

On The Reconstruction Of An Integro-Differential Dirac Operator With Parameter-Dependent Nonlocal Integral Boundary Conditions From The Nodal Data, Baki Keskin, Yu Ping Wang

Turkish Journal of Mathematics

We consider the integro-differential Dirac operator with parameter-dependent nonlocal integral boundary conditions. We derive the asymptotic expressions for the eigenvalues and the zeros of eigenfunctions (nodal points or nodes) and develop a constructive procedure for solving the inverse nodal problem for this operator.


Isometries Of Length 1 In Purely Loxodromic Free Kleinian Groups And Trace Inequalities, İlker Savaş Yüce, Ahmet Nedi̇m Narman Mar 2024

Isometries Of Length 1 In Purely Loxodromic Free Kleinian Groups And Trace Inequalities, İlker Savaş Yüce, Ahmet Nedi̇m Narman

Turkish Journal of Mathematics

In this paper, we prove a generalization of a discreteness criteria for a large class of subgroups of PSL2(C) . In particular, given a finitely generated purely loxodromic free Kleinian group Γ = ⟨ξ1, ξ2, . . . , ξn⟩ for n ≥ 2, we show that |trace2(ξi) − 4| + |trace(ξiξjξ −1 i ξ −1 j ) − 2| ≥ 2 sinh2 ( 1 4 log αn ) for some ξi and ξj for i ̸= j in Γ provided that certain conditions on the hyperbolic displacements given by ξi , ξj and their length 3 conjugates formed by …


On The Oscillation And Asymptotic Behavior Of Solutions Of Third Order Nonlineardifferential Equations With Mixed Nonlinear Neutral Terms, Shaimaa Salem, Mohamed M. A. El-Sheikh, Ahmed Mohamed Hassan Mar 2024

On The Oscillation And Asymptotic Behavior Of Solutions Of Third Order Nonlineardifferential Equations With Mixed Nonlinear Neutral Terms, Shaimaa Salem, Mohamed M. A. El-Sheikh, Ahmed Mohamed Hassan

Turkish Journal of Mathematics

This paper is concerned with the oscillation and asymptotic behavior of solutions of third-order nonlinear neutral differential equations with a middle term and mixed nonlinear neutral terms in the case of the canonical operator. We establish several oscillation criteria that guarantee that all solutions are oscillatory or converge to zero. The given results are obtained by applying the comparison method, the Riccati transformation and the integral averaging technique. The results improve significantly and extend existing ones in the literature. Finally, illustrative examples are given.


Modules Over Invertible 1-Cocycles, José Manuel Fernández Vilaboa, Ramon Gonzalez Rodriguez, Brais Ramos Pérez, Ana Belén Rodríguez Raposo Mar 2024

Modules Over Invertible 1-Cocycles, José Manuel Fernández Vilaboa, Ramon Gonzalez Rodriguez, Brais Ramos Pérez, Ana Belén Rodríguez Raposo

Turkish Journal of Mathematics

In this paper, we introduce in a braided setting the notion of left module for an invertible 1-cocycle and we prove some categorical equivalences between categories of modules associated to an invertible 1-cocycle and categories of modules associated to Hopf braces.


An Extension Of The Definition On The Compositions Of The Singular Distributions, Emi̇n Özçağ Mar 2024

An Extension Of The Definition On The Compositions Of The Singular Distributions, Emi̇n Özçağ

Turkish Journal of Mathematics

Gelfand and Shilov give the definition of the composition δ(g(x)) for an infinitely differentiable function g(x) having any number of simple roots. In the paper, we consider their definition for an infinitely differentiable function having any number of multiple roots by using the method of the discarding of unwanted infinite quantities from asymptotic expansions and give some examples. Further, we define the compositions δ(g+) and δ(g−) for a locally summable function g(x).


Qualitative Results For A Generalized 2-Component Camassa-Holm System With Weak Dissipation Term, Nurhan Dündar Mar 2024

Qualitative Results For A Generalized 2-Component Camassa-Holm System With Weak Dissipation Term, Nurhan Dündar

Turkish Journal of Mathematics

Our main aim in the current study is to examine the mathematical properties of a generalized 2-component Camassa-Holm system with a weakly dissipative term. Firstly, we acquire the theorem of well-posedness in locally for the generalized system with weak dissipation. Then, we demonstrate that this system can reveal the blow-up phenomenon. Finally, we acquire the theorem of global existence utilizing a method of the Lyapunov function.


Lightcone Framed Curves In The Lorentz-Minkowski 3-Space, Liang Chen, Masatomo Takahashi Mar 2024

Lightcone Framed Curves In The Lorentz-Minkowski 3-Space, Liang Chen, Masatomo Takahashi

Turkish Journal of Mathematics

For a nonlightlike nondegenerate regular curve, we have the arc-length parameter and the Frenet-Serret type formula by using a moving frame like a regular space curve in the Euclidean space. If a point of the curve moves between spacelike and timelike regions, then there is a lightlike point. In this paper, we consider mixed types of not only regular curves but also curves with singular points. In order to consider mixed type of curves with singular points, we introduce a frame, so-called the lightcone frame, and lightcone framed curves. We investigate differential geometric properties of lightcone framed curves.


Timelike Surfaces With Parallel Normalized Mean Curvature Vector Field In The Minkowski 4-Space, Victoria Bencheva, Velichka Milousheva Mar 2024

Timelike Surfaces With Parallel Normalized Mean Curvature Vector Field In The Minkowski 4-Space, Victoria Bencheva, Velichka Milousheva

Turkish Journal of Mathematics

In the present paper, we study timelike surfaces with parallel normalized mean curvature vector field in the four-dimensional Minkowski space. We introduce special isotropic parameters on each such surface, which we call canonical parameters, and prove a fundamental existence and uniqueness theorem stating that each timelike surface with parallel normalized mean curvature vector field is determined up to a rigid motion in the Minkowski space by three geometric functions satisfying a system of three partial differential equations. In this way, we minimize the number of functions and the number of partial differential equations determining the surface, thus solving the Lund-Regge …