The string tensions can be dynamical as one of us (EG) has studied in recent publications. For example, in the case when string theories are formulated in the modified measure formalism where string and brane tensions appear as an additionaldynamical degree of freedom. It is found that the tension values assigned to these strings and branes may not fixed (universal), but rather that each string and brane acquires its own tension with a different value for each string and brane. We havedisplayed cases where the spontaneous breaking of target space scale invariance is produced in the process of string-tension-generation, except for some limits where the tensions dynamically approach infinity. The introduction of internal gauge fieldsgoverns the dynamical tensions of the strings, and specific sources for these gauge fields provide diverse tensions. In this work it is shown that in special cases where the tensions have the exponential form exp(ασ1) or exp(ασ0), in the conformal gauge, the target space scale invariance can be restored by considering shifts in either the (spatial) σ1 or (temporal) σ0 string world-sheet coordinates. In the first case, the (open) strings must be of infinite length and cannot have boundaries in order to respect target space scaleinvariance. While in the second case we can consider closed or open strings without breaking target space scale invariance. World sheet conformal invariance implies a Ricci flat condition for an effective metric and which is consistent with the expected equations of motion of the strings. Boundary conditions can be introduced by introducing charges that couple to the internal gauge fields. Point like sources break the scale invariance point-wise which can lead to very interesting consequences, like the construction ofsemi-open strings which are strings which connect to a charge only at one point and where along the other direction the tension decays. These serve as models of deconfined quarks. Generalizations of these effects to brane like solutions in Milne and Wesson spaces, etc. are also discussed.