Earlier Paper Research Articles

Cupping Therapy (حجامه) in the view of Islamic teaching

The term "cupping therapy" refers to treatments that involve applying sucking cups to specific skin regions for therapeutic reasons. Cupping therapy is a straightforward, risk-free, comfortable, efficient, cost-effective, and time-saving procedure. Traditional wet cupping therapy is a two-step process that involves cupping first, then superficially scarifying the skin (also known as the double S technique). Traditional wet cupping therapy was found to be successful in treating carpal tunnel syndrome in a German study. Al-hijamah is a three-step method that involves wet cupping therapy in prophetic medicine (suction, scarification, and suction technique, ie, triple S technique). According to the evidence-based Taibah mechanism, al-hijamah is a successful excretory therapy that purges the blood and interstitial spaces of harmful pathogenic chemicals. we firmly advocated Al-hijamah in our earlier articles for normal medical practice in hospitals. Al-hijamah was strongly advised for the treatment of thalassemia. In healthy people, al-hijamah dramatically reduced serum ferritin levels. Al-hijamah is an excretory procedure that considerably purges blood of harmful chemicals. Thalassemia may be a good candidate for treatment with Al-hijamah to remove extra iron and ferritin from thalassemic blood (via percutaneous iron excretion), as we mentioned in earlier papers. Al-hijamah is a brand-new percutaneous iron excretion therapy (PIET), which we will explore in this article. Interestingly, despite their distinct etiologies and pathophysiology, autoimmune disorders and migraine headaches responded favorably to al-hijamah treatment.

A COMBINATORIAL TRANSLATION PRINCIPLE AND DIAGRAM COMBINATORICS FOR THE GENERAL LINEAR GROUP

Let k be an algebraically closed field of characteristic p > 0. We compute the Weyl filtration multiplicities in indecomposable tilting modules and the decomposition numbers for the general linear group over k in terms of cap diagrams under the assumption that p is bigger than the greatest hook length in the partitions involved. Then we introduce and study the rational Schur functor from a category of GLn-modules to the category of modules for the walled Brauer algebra. As a corollary, we obtain the decomposition numbers for the walled Brauer algebra when p is bigger than the greatest hook length in the partitions involved. This is a sequel to an earlier paper on the symplectic group and the Brauer algebra.

Can tetraphenylethane (TPE) “iniferter” groups be introduced into polymer chains by coupling TPE diol with diisocyanates?

Several different articles have appeared in recent years concerning the application of tetraphenylethane (TPE) groups, which are able to dissociate to free radicals under mild heating, for the initiation of radical polymerization of vinyl monomers. It has been claimed that the TPE group is introduced into the polymer chain by the reaction of 1,1,2,2-tetraphenyl-1,2-ethanediol (TPED) with diisocyanate, optionally with the application of the additional oligodiol. This approach is based on the presumed reaction of the isocyanate group with a tertiary hydroxyl group that is supposed to form urethane linkages. In the present study, we checked whether such a reaction can indeed occur under the applied conditions. A kinetic study of the reaction of poly(tetrahydrofuran) diol plus TPED or polylactide diol plus TPED with diisocyanate (aromatic or aliphatic) was performed in two different solvents, and conversion of isocyanate groups was followed by FT IR spectroscopy. Independently, the kinetics of the reaction of TPED alone with diisocyanates were investigated. The products of the reactions were analyzed by the 1H NMR method for the expected consumption of tertiary –OH groups and urethane bond formation. Theoretical calculations for the reactivity of tertiary –OH groups in TPED with isocyanate groups are presented as additional proof that this reaction should not proceed under the conditions applied in earlier papers. A new approach to the introduction of TPE units into polymer structures is suggested.

Housing loan default in Malaysia: an analytical insight and policy implications

PurposeThe purpose of this paper is to examine the drivers of default in the Malaysian housing market in the light of various policy interventions by the country’s central bank, and the government’s expressed concern to ensure balanced growth in the market. This paper assesses the importance of considering the endogeneity of loan-to-value (LTV) in predicting housing loan default and its implications.Design/methodology/approachIn this paper, the author addresses the endogeneity problem in the LTV variable using two instrumental variables (IV) in this probit regression: national residential property gains tax and the statutory reserve ratio of Bank Negara Malaysia. This study uses the instrumental variable probit model to consider endogeneity bias. This study assumes a latent (unobservable) variable (Y*), representing a borrower’s tendency to default, which is associated linearly with the borrower’s and loan characteristics and other variables (Xi). This study uses individual borrower-level information of 43,156 housing loan borrowers from the files of a well-established housing bank in Malaysia.FindingsThis study’s results confirm that endogeneity causes a substantial difference in the magnitude of the estimated effects of LTV on the default tendency. At the lower values of LTV, the probability of default is over-estimated, and at the higher values, the default probability is substantially underestimated. Endogeneity bias also affects the estimated coefficients of loan and borrower characteristics. The authors find that the interest rate is less relevant in predicting loan default. Other loan characteristics, such as loan age, tenure, payment amount and the built-up area, are relevant. This study’s result confirms that the borrower’s location matters, and an increase in state gross domestic product per capita and an increase in the supply of residential units reduce default probability.Research limitations/implicationsThe present study did not explore the applicability of the “equity theory of default” in the Malaysian housing market. This study did not assess “strategic default” issues and the effect of borrowers’ characteristics, personality traits and self-control of Malaysian housing loan borrowers in the mortgage decision-making process. The evolving dynamics of the Malaysian housing market microstructure in property valuation remained unexplored in the present study.Practical implicationsThe findings have crucial relevance in the decision-making process of commercial banks, the central bank and the government to frame policies to foster balanced growth and development in the housing market. The authors argue that striking a subtle balance between the concerns of financial stability and productive risk-taking by commercial banks in Malaysia remains a continuing challenge for the country’s central bank. The authors also argue that designing suitable taxation policies by the government can deliver its cherished goal of balanced development in the housing market.Originality/valueEmpirical research on the Malaysian housing market based on micro-level data is scarce due to a paucity of relevant data. This study is based on the individual borrower-level information of 43,156 housing loan borrowers from the files of a well-established housing bank in Malaysia. In this analysis, the authors find clear evidence of endogeneity in LTV and argue that any attempts to decipher the default drivers of housing loans without addressing the issue of endogeneity may lead to faulty interpretation. Therefore, this study is unique in recognizing endogeneity and has gone deeper in identifying the default drivers in the Malaysian housing market not addressed by earlier papers.

Addendum: Painlevé transcendents and -symmetric Hamiltonians (2015 J. Phys. A: Math. Theor. 48 475202)

This paper is an Addendum to reference Bender and Komijani (2015 J. Phys. A: Math. Theor. 48 475202) (which stems from an earlier paper Bender et al (2014 J. Phys. A: Math. Theor. 47 235204)), where it was demonstrated that unstable separatrix solutions to the Painlevé equations I and II are determined by -symmetric Hamiltonians. Here, unstable separatrix solutions of the fourth Painlevé transcendent are studied numerically and analytically. It is shown that for a fixed initial value such as y(0) = 1 a discrete set of initial slopes y′(0) = b n give rise to separatrix solutions. Similarly, for a fixed initial slope such as y′(0) = 0 a discrete set of initial values y(0) = c n give rise to separatrix solutions. For Painlevé IV the large-n asymptotic behavior of b n is b n ∼ B IV n 3/4 and that of c n is c n ∼ C IV n 1/2. The constants B IV and C IV are determined both numerically and analytically. The analytical values of these constants are found by reducing the nonlinear Painlevé IV equation to the linear eigenvalue equation for the sextic -symmetric Hamiltonian .

The local hole: a galaxy underdensity covering 90 per cent of sky to ≈200 Mpc

ABSTRACT We investigate the ‘Local Hole’, an anomalous underdensity in the local galaxy environment, by extending our previous galaxy K-band number-redshift and number-magnitude counts to ≈90 per cent of the sky. Our redshift samples are taken from the 2MASS Redshift Survey (2MRS) and the 2M++ catalogues, limited to K < 11.5. We find that both surveys are in good agreement, showing an $\approx 21\!-\!22{{\ \rm per\ cent}}$ underdensity at z < 0.075 when compared to our homogeneous counts model that assumes the same luminosity function (LF) and other parameters as in our earlier papers. Using the Two Micron All Sky Survey (2MASS) for n(K) galaxy counts, we measure an underdensity relative to this model of $20 \pm 2 {{\ \rm per\ cent}}$ at K < 11.5, which is consistent in both form and scale with the observed n(z) underdensity. To examine further the accuracy of the counts model, we compare its prediction for the fainter n(K) counts of the Galaxy and Mass Assembly (GAMA) survey. We further compare these data with a model assuming the parameters of a previous study where little evidence for the Local Hole was found. At 13 < K < 16, we find a significantly better fit for our galaxy counts model, arguing for our higher LF normalization. Although our implied underdensity of $\approx 20{{\ \rm per\ cent}}$ means local measurements of the Hubble Constant have been overestimated by ≈3 per cent, such a scale of underdensity is in tension with a global ΛCDM cosmology at an ≈3σ level.

A Wideband Satellite Maritime Channel Model Simulator

In this article, we present implementation details of a generative satellite maritime propagation channel model at L-band. In an earlier paper, we presented the parameterization of the channel model for the narrowband case based on recordings of GPS L1 <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$C/N_{0}$ </tex-math></inline-formula> time-series in different sea state conditions. Additionally, we performed wider band measurements using GPS E5a (≈10 Mcps—chips per second— > 20 MHz bandwidth) and obtained estimations of power delay profiles. Due to lack of dynamic range and delay resolution, in these measurements, no conclusive information was gathered on the time spreading caused by the channel. What was clear is that the time spreading was not significant outside the first signal chip, i.e., <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\approx 0.1~\mu \text{s}$ </tex-math></inline-formula> . Still wideband modeling is required within this spreading range. Now, we want to extend the model to the wideband case. To achieve this goal, we have used a rough surface scattering model applicable to sea surfaces and employed it to characterize the time dispersion to be expected. Additionally, we also used this scattering model to help verify the validity of the existing Doppler spread model. Furthermore, ship movements in the waves play a role. We try and analyze this issue. Finally, we present a detailed discussion on various implementation issues we came across when coding the simulator.

Non-Hamiltonian Actions With Fewer Isolated Fixed Points

Abstract In an earlier paper, the second author resolved a question of McDuff by constructing a non-Hamiltonian symplectic circle action on a closed, connected six-dimensional symplectic manifold with exactly 32 fixed points. In this paper, we improve on this example by reducing the number of fixed points. More concretely, we construct a non-Hamiltonian symplectic circle action on a closed, connected six-dimensional symplectic manifold with exactly $2k$ fixed points for any $k \geq 5$.

Using Nemirovski's Mirror-Prox method as basic procedure in Chubanov's method for solving homogeneous feasibility problems

We introduce a new variant of Chubanov's method for solving linear homogeneous systems with positive variables. In the Basic Procedure we use a recently introduced cut in combination with Nemirovski's Mirror-Prox method. We show that the cut requires at most time, just as Chubanov's cut. In an earlier paper it was shown that the new cuts are at least as sharp as those of Chubanov. Our Modified Main Algorithm is in essence the same as Chubanov's Main Algorithm, except that it uses the new Basic Procedure as a subroutine. The new method has time complexity, where is a suitably defined condition number. As we show, a simplified version of the new Basic Procedure competes well with the Smooth Perceptron Scheme of Peña and Soheili and, when combined with Rescaling, also with two commercial codes for linear optimization.

Some Remarks on the Saito Kurokawa Lift for Orthogonal Forms

Duke and Imamoglu showed that the Saito–Kurokawa lift for Siegel modular forms can in an elegant manner be obtained from a converse theorem by Imai using spectral analysis of the hyperbolic Laplacian. In an earlier paper we gave a simplified approach without any appeal to spectral analysis. Here we want to show, that this generalizes to some orthogonal groups of signature (2,m+2) with m>2.

A scattering problem for a local perturbation of an open periodic waveguide

In this paper, we consider the propagation of waves in an open waveguide in where the index of refraction is a local perturbation of a function which is periodic along the axis of the waveguide (which we choose to be the x1 axis) and equal to one for |x2| &gt; h0 for some h0 &gt; 0. Motivated by the limiting absorption principle (proven in an earlier paper by the author), we formulate a radiation condition which allows the existence of propagating modes and prove uniqueness, existence, and stability of a solution under the assumption that no bound states exist. In the second part, we determine the order of decay of the radiating part of the solution in the direction of the layer and in the direction orthogonal to it. Finally, we show that it satisfies the classical Sommerfeld radiation condition and allows the definition of a far field pattern.

The Witten index and the spectral shift function

In [Spectral asymmetry and Riemannian geometry. III, Math. Proc. Cambridge Philos. Soc. 79 (1976) 71–99] Atiyah, Patodi and Singer introduced spectral flow for elliptic operators on odd-dimensional compact manifolds. They argued that it could be computed from the Fredholm index of an elliptic operator on a manifold of one higher dimension. A general proof of this fact was produced by Robbin–Salamon [The spectral flow and the Maslov index, Bull. London Math. Soc. 27(1) (1995) 1–33, MR 1331677]. In [F. Gesztesy, Y. Latushkin, K. Makarov, F. Sukochev and Y. Tomilov, The index formula and the spectral shift function for relatively trace class perturbations, Adv. Math. 227(1) (2011) 319–420, MR 2782197], a start was made on extending these ideas to operators with some essential spectrum as occurs on non-compact manifolds. The new ingredient introduced there was to exploit scattering theory following the fundamental paper [A. Pushnitski, The spectral flow, the Fredholm index, and the spectral shift function, in Spectral Theory of Differential Operators, American Mathematical Society Translations: Series 2, Vol. 225 (American Mathematical Society, Providence, RI, 2008), pp. 141–155, MR 2509781]. These results do not apply to differential operators directly, only to pseudo-differential operators on manifolds, due to the restrictive assumption that spectral flow is considered between an operator and its perturbation by a relatively trace-class operator. In this paper, we extend the main results of these earlier papers to spectral flow between an operator and a perturbation satisfying a higher pth Schatten class condition for [Formula: see text], thus allowing differential operators on manifolds of any dimension [Formula: see text]. In fact our main result does not assume any ellipticity or Fredholm properties at all and proves an operator theoretic trace formula motivated by [M.-T. Benameur, A. Carey, J. Phillips, A. Rennie, F. Sukochev and K. Wojciechowski, An analytic approach to spectral flow in von Neumann algebras, in Analysis, Geometry and Topology of Elliptic Operators (World Scientific Publisher, Hackensack, NJ, 2006), pp. 297–352, MR 2246773; A. Carey, H. Grosse and J. Kaad, On a spectral flow formula for the homological index, Adv. Math. 289 (2016) 1106–1156, MR 3439708]. We illustrate our results using Dirac type operators on [Formula: see text] for arbitrary [Formula: see text] (see Sec. 8). In this setting Theorem 6.4 substantially extends Theorem 3.5 of [A. Carey, F. Gesztesy, H. Grosse, G. Levitina, D. Potapov, F. Sukochev and D. Zanin, Trace formulas for a class of non-Fredholm operators: a review, Rev. Math. Phys. 28(10) (2016) 1630002, MR 3572626], where the case d = 1 was treated.

Does an Empirical Economic Relation Have a Life?

Does an Empirical Economic Relation Have a Life?

Loan to value ratio and housing loan default – evidence from microdata in India

PurposeThis study aims to investigate the factors that drive housing loan default in India based on unique micro-level data drawn from a public sector bank's credit files with a national presence in India. The authors address endogeneity in the loan to value ratio (LTV) while deciphering the drivers of default.Design/methodology/approachThe study uses a probit regression approach to analyze the relationship between the probability of default and the explanatory variables. The authors introduce two instrumental variables to address the issue of endogeneity. The authors also add state-level demographic and several other control variables, including an indicator variable that captures the recent regulatory change. The authors’ analysis is based on 102,327 housing loans originated by the bank between January 2001 and December 2017.FindingsThe authors find that addressing the endogeneity issue is essential to specify default drivers, especially LTV, correctly. The nature of employment, gender, socio-religious category and age have a distinct bearing on housing loan defaults. Apart from the LTV ratio, the other key determinants of default are the interest rate, frequency of repayment, prepayment options and the loan period. The findings suggest that the population classification of branch location plays a significant role in loan default. The authors find that an increase in per capita income and an increase in the number of employed people in the state, which reflects borrowers' ability to pay by borrowers, reduce the probability of default. The change in the regulatory classification of loan assets by the Reserve Bank of India did not bear the main results.Research limitations/implicationsThe non-availability of the house price index in analyzing the default dynamics in the Indian housing finance market for the period covered under the study has constrained our analysis. The applicability of the equity theory of default, strategic default, borrowers' characteristics and personality traits are potential research areas in the Indian housing finance market.Practical implicationsThe study's findings are expected to provide valuable inputs to the banks and the housing finance companies to explore and formulate appropriate strategic options in lending to this sector. It has highlighted various vistas of tailor-making housing loan product offerings by the commercial banks to ensure and steady and healthy growth of their loan portfolio. It has also highlighted the regulatory and policy underpinnings to ensure the healthy growth of the Indian housing finance market.Originality/valueThe study provides a fresh perspective on the default drivers in the Indian housing finance market based on micro-level data. In our analysis, the authors find clear evidence of endogeneity in LTV and argue that any attempts to decipher the default drivers of housing loans without addressing the issue of endogeneity may lead to faulty interpretation. Therefore, this study is unique in recognizing endogeneity and has gone deeper in identifying the default drivers in the Indian housing market not addressed by earlier papers on the Indian housing market. The authors also control for the regulatory changes in the Indian housing finance market and include state-level control variables like per capita GDP and the number of workers per thousand to capture the borrowers' ability to pay characteristics.

Extended Literature Review of the role of erythropoietin stimulating agents (ESA) use in the management of post renal transplant anaemia

Background: Anemia is known to impact quality of life and survival in both renal and non-renal patients. End stage kidney disease (ESKD) patient's survival substantially improves post transplantation. Observational studies have reported better patients and graft outcomes in non anemic renal transplant recipients. Anemia of chronic kidney disease (CKD) is frequently linked to erythropoietin deficiency. Patients with post-transplant anemia (PTA) represent a distinct subset of CKD population. The benefit of using erythropoietin stimulating agents (ESA) in PTA is not clearly defined. Aim: The aim of this extended literature review is to define the role of ESA use in improving hemoglobin (Hb) level and graft survival in patients with PTA. Methods: An extended literature review was done to identify randomized controlled trials (RCTs) with patients with PTA as the study population, the use of erythropoietin stimulating agents as the intervention, and the renal function and Hb level as the outcomes. The aim of this literature review is to delineate the role of using ESA in PTA. Medline, Google scholar, Scopus, and CINHAL data bases were searched and papers meeting the pre-set inclusion criteria were identified. Results: A total of 163 papers were identified. After screening the results, four papers met the inclusion criteria and were included for review. 2/4 papers recruited patients with early PTA, while 2/4 papers recruited patients with late PTA. The early PTA papers were not consistent in reporting the effect of ESA in improving renal outcomes. Both studies showed that using ESA had no additional benefit in anemia treatment. 2/4 studies looked at late PTA. The study designs were similar and the follow up period was 2-3 years. Both studies showed a better graft survival in the higher Hb group. Conclusion: In the case of early PTA, the benefit of using ESA is not clear. The two RCTs studying the effect of ESA in patients with late PTA showed that targeting higher Hb levels was associated with better graft function. The optimal Hb target and the utility of intravenous iron need further clarifications.

Primordial Black Holes from Collapsing Antimatter

In this paper a simple (i.e. free of fine-tuning, etc.) new mechanism for primordial black hole formation based on the collapse of large antimatter systems in the early Universe is introduced. A peculiarity of this process is that, compared to their material counterparts, the collapse of large antimatter systems takes much less time due to the reversed thermodynamics of antimatter, an idea which has been proposed in our earlier paper Etesi (2021). This model has several testable predictions. The first is that the photon-baryon ratio is roughly computable and is equal to 3.03times 10^9 which is quite close to its experimentally confirmed value. The second is that the mass of black holes arising from this mechanism is at least 10^5-10^6M_odot hence they contribute to the super- or hypermassive end of the primordial black hole mass spectrum. The third prediction is that these sort of primordial black holes constitute at least 20% of dark matter. Last but not least the observed current asymmetry of matter and antimatter, even if their presence in the Universe was symmetric in the beginning, acquires a natural explanation, too.

Postscript

There has been a ruling in December 2021 by the High Court in New Zealand that data to do with vaccination be given over by the Ministry of Health to the Whānau Ora Commissioning Agency. The present article, Ngā Pakanga Maramara, The Data Wars, forms a Postscript to Maramara me te Iwi, Data and the Indigenous Group, an earlier paper in tekaharoa.com and takes the argument therein to a consideration of this ruling and the context involved. A similar form is followed to that of the earlier paper and in the example of the High Court ruling and its aftermath concepts of state and ethnicity are considered along with an overview of government and Iwi organisations in Aotearoa-New Zealand. The ruling is considered as something of a change or a breakthrough to new forms of data control. The nature and use of data is considered in general terms as well as in the specific context of the Covid 19 pandemic in Aotearoa-New Zealand. There is considerable discussion of border concepts and practices as there is of mental as well as physical health.

Intensification of Tilted Tropical Cyclones over Relatively Cool and Warm Oceans in Idealized Numerical Simulations

Abstract A cloud-resolving model is used to examine the intensification of tilted tropical cyclones from depression to hurricane strength over relatively cool and warm oceans under idealized conditions where environmental vertical wind shear has become minimal. Variation of the SST does not substantially change the time-averaged relationship between tilt and the radial length scale of the inner core, or between tilt and the azimuthal distribution of precipitation during the hurricane formation period (HFP). By contrast, for systems having similar structural parameters, the HFP lengthens superlinearly in association with a decline of the precipitation rate as the SST decreases from 30° to 26°C. In many simulations, hurricane formation progresses from a phase of slow or neutral intensification to fast spinup. The transition to fast spinup occurs after the magnitudes of tilt and convective asymmetry drop below certain SST-dependent levels following an alignment process explained in an earlier paper. For reasons examined herein, the alignment coincides with enhancements of lower–middle-tropospheric relative humidity and lower-tropospheric CAPE inward of the radius of maximum surface wind speed rm. Such moist-thermodynamic modifications appear to facilitate initiation of the faster mode of intensification, which involves contraction of rm and the characteristic radius of deep convection. The mean transitional values of the tilt magnitude and lower–middle-tropospheric relative humidity for SSTs of 28°–30°C are respectively higher and lower than their counterparts at 26°C. Greater magnitudes of the surface enthalpy flux and core deep-layer CAPE found at the higher SSTs plausibly compensate for less complete alignment and core humidification at the transition time.

Calculated versus measured iron losses and instantaneous magnetization power functions of electrical steel

Magnetic energy loss P of soft magnetic laminations like SiFe sheets tends to be expressed through an integral over the power product H · dB/dt. Already in earlier papers, we stressed that distinctions are needed for the quantities H and B. However, they are not considered in practically consistent ways, in the so far literature. Here, we discuss these distinctions in closer ways, comparing loss determination by calculation and measurement, respectively. A physically consistent procedure is described for the determination of loss and magnetization power functions through measurement of bi-located quantities HS and BC (S surface, C cross section). On the other hand, it is concluded that corresponding quantitative calculations—based on co-located quantities H and B—are impeded by the high amount of technological parameters of modern steel products. For example, they result from chemical additions, and—in particular—also from specific technologies of rolling, annealing, coating or scribing.

Homogeneous Banach Spaces as Banach Convolution Modules over M(G)

This paper is supposed to form a keystone towards a new and alternative approach to Fourier analysis over LCA (locally compact Abelian) groups G. In an earlier paper the author has already shown that one can introduce convolution and the Fourier–Stieltjes transform on (M(G),∥·∥M), the space of bounded measures (viewed as a space of linear functionals) in an elementary fashion over Rd. Bounded uniform partitions of unity (BUPUs) are easily constructed in the Euclidean setting (by dilation). Moving on to general LCA groups, it becomes an interesting challenge to find ways to construct arbitrary fine BUPUs, ideally without the use of structure theory, the existence of a Haar measure and even Lebesgue integration. This article provides such a construction and demonstrates how it can be used in order to show that any so-called homogeneous Banach space(B,∥·∥B) on G, such as (Lp(G),∥·∥p), for 1≤p&lt;∞, or the Fourier–Stieltjes algebra FM(G), and in particular any Segal algebra is a Banach convolution module over (M(G),∥·∥M) in a natural way. Via the Haar measure we can then identify L1(G),∥·∥1 with the closure (of the embedded version) of Cc(G), the space of continuous functions with compact support, in (M(G),∥·∥M), and show that these homogeneous Banach spaces are essentialL1(G)-modules. Thus, in particular, the approximate units act properly as one might expect and converge strongly to the identity operator. The approach is in the spirit of Hans Reiter, avoiding the use of structure theory for LCA groups and the usual techniques of vector-valued integration via duality. The ultimate (still distant) goal of this approach is to provide a new and elementary approach towards the (extended) Fourier transform in the setting of the so-called Banach–Gelfand triple(S0,L2,S0′)(G), based on the Segal algebra S0(G). This direction will be pursued in subsequent papers.